ANTIBACTERIAL COMPOUNDS, THEIR PRODUCTION AND USE

Abstract: A compound of the formula; wherein R¹ is an amino group which may be protected, R³ is a hydrogen atom or an optionally substituted hydrocarbon residue; Z is S, S → O, O or CH₂, R⁴ is a hydrogen atom, methoxy group or formamido group, R¹³ is a hydrogen atom, methyl group, hydroxyl group or halogen atom and A ⊕ is an optionally substituted imidazolium-1-yl group forming a con­ densed ring at the 2,3-or 3,4-position or a pharmaceutically acceptable salt or ester thereof is novel and has excellent antibacterial activity.

Description: This invention relates to novel antibacterial compounds having excellent antibacterial action, a method of preparing the same and a pharmaceutical composition containing the same. A variety of cephem compounds having a quaternary ammoniomethyl group at the 3-position and 2-(2-aminothiazol-4-yl)-2-hydroxy(or substituted hydroxy)iminoacetamido group at the 7-position simultaneously have so far been synthesized, and patent applications (for instance Japanese Publication of Unexamined Application (Kokai) Sho-53-34795, Sho-54-9296, Sho-54-135792, Sho-54-154786, Sho-55-149289, Sho-57-56485, Sho-57-192394, Sho-58-159498 etc.) concerning those compounds have been published. However, most of the compounds, whose quaternary ammoniomethyl group at the 3-position has a nitrogen-containing aromatic heterocyclic ring, are those having a monocyclic pyridinium group with or without a substituent or substituents on the ring thereof, and the compounds of the present invention having an imidazolium-1-yl group which forms a condensed ring at the 2,3-position or the 3,4-position have never been disclosed in the specification of any patent application, not to speak of a report of the synthesis thereof. Cephem-type antibiotics have been widely used for the therapy of diseases of human beings and animals caused by pathogenic bacteria. These compounds are especially useful for the therapy of diseases caused by bacteria resistant to penicillin-type antibiotics as well as for the therapy of penicillin-sensitive patients. In these cases, it is desirable to use cephem-type antibiotics showing activity against both gram-positive and gram-negative bacteria. For this reason, extensive studies on cephem-type antibiotics having a wide antibacterial spectrum have been carried out. As a result of research work covering a long period of time, it has been found that introduction of 2-(2-aminothiazol-4-yl)-2-hydroxy (or substituted hydroxy)iminoacetamido group or nitrogen-containing heterocycle-amino group at the 7-position of cephem ring renders the cephem compound active against both gram-positive and gram-negative bacteria, which has led to the exploitation and development of what is called "the third generation cephalosporin". At present, several types of the third generation cephalosporin compounds have already been put on the market. Another characteristic feature of these third generation cephalosporin antibiotics lies in that these substances are active against the so-called cephalosporin-resistant bacteria, which penicillins have also encountered. More specifically, cephem compounds of the third generation showed antibacterial action to such an extent as to make them clinically usable against some strains of Escherichia coli , some of the bacteria belonging to the genus Citrobacter and most of the bacteria belonging to the genus Proteus that are positive to indole reactions as well as against most of the pathogenic bacteria classified into the genus Enterobacter , Serratia or Pseudomonas . However, the third generation cephalosporin compounds are not always satisfactory. Their antibacterial activities for example against Pseudomonas are not satisfactorily strong. The present invention relates to a compound of the formula wherein R¹ is an amino group or an amino group protected by a conventional protective group; R³ is a hydrogen atom or a hydrocarbon residue optionally substituted by one to three of hydroxyl, C₁₋₆ alkyl, C₂₋₆ alkenyl, C₂₋₆ alkynyl, C₃₋₁₀ cycloalkyl, C₅₋₆ cycloalkenyl, C₆₋₁₀ aryl, C₇₋₁₉ aralkyl, a 5 to 8-membered ring containing one to four heteroatoms of nitrogen atom which may optionally be oxidized, oxygen atom, sulfur atom or a fused ring thereof, C₁₋₆ alkoxy, c₃₋₁₀ cycloalkyloxy, C₆₋₁₀ aryloxy, C₇₋₁₉ aralkyloxy, thiazolyloxy, mercapto, C₁₋₆ alkylthio, C₃₋₁₀ cycloalkylthio, C₆₋₁₀ arylthio, C₇₋₁₉ aralkylthio, thiazolylthio, amino, mono-C₁₋₆ alkylamino, di-C₁₋₆ alkylamino, tri-C₁₋₆ alkylammonium, C₃₋₁₀ cycloalkylamino, C₆₋₁₀ arylamino, C₇₋₁₉ aralkylamino, thiazolylamino, thiadiazolylamino, cyclic amino, azido, nitro, halogen, cyano, carboxyl, C₁₋₁₀ alkoxy-carbonyl, C₆₋₁₀ aryloxycarbonyl, C₇₋₁₉ aralkyloxy-carbonyl, benzoyl, naphthoyl, phthaloyl, phenylacetyl, C₁₋₆ alkanoyl, c₃₋₅ alkenoyl, benzoyloxy, naphthoyloxy, phenylacetoxy, C₂₋₆ alkanoyloxy, c₃₋₅ alkenoyloxy, carbamoyl, N-methylcarbamoyl, N,N-dimethylcarbamoyl, N-ethylcarbamoyl, N,N-diethylcarbamoyl, N-phenylcarbamoyl, N-acetylcarbamoyl, N-benzoylcarbamoyl, N-(p-methoxy-phenyl)carbamoyl, pyrrolidinocarbonyl, piperidinocarbonyl, piperazinocarbonyl, morpholinocarbonyl, thiocarbamoyl, N-methylthiocarbamoyl, N-phenylthiocarbamoyl, carbamoyloxy, N-methylcarbamoyloxy, N,N-dimethylcarbamoyloxy, N-ethylcarbamoyloxy, N-phenylcarbamoyloxy, phthalimido, C₁₋₆ alkanoylamino, benzamido, naphthoylamido, phthalimido, carboxyamino, C₁₋₁₀ alkoxy-carboxamido, C₆₋₁₀ aryloxycarboxamido or C₇₋₁₉ aralkyloxy-carboxamido; Z is S, S -> O, O or CH₂; R⁴ is a hydrogen atom, methoxy group or formamido group; R¹³ is a hydrogen atom, methyl group, hydroxyl group or halogen atom and A⁺ is an imidazolium-1-yl group forming a fused ring at the 2,3- or 3,4-position that is optionally substituted by one or two of hydroxyl group, hydroxy C₁₋₆ alkyl group, C₁₋₆ alkyl group, C₂₋₆ alkenyl group, c₂₋₆-alkynyl group, C₄₋₆ alkadienyl group, C₃₋₁₀ cycloalkyl group, C₅₋₆ cycloalkenyl group, C₃₋₁₀ cycloalkyl C₁₋₆ alkyl group, C₆₋₁₀ aryl group, C₇₋₁₂ aralkyl group, di-C₆₋₁₀ aryl-methyl group, tri-C₆₋₁₀ arylmethyl group, a 5 to 8-membered ring containing one to four heteroatoms of nitrogen atom which may optionally be oxidized, oxygen atom, sulfur atom or a fused ring thereof, c₁₋₆ alkoxy group, C₁₋₆ alkoxy C₁₋₆ alkyl group, c₃₋₁₀ cycloalkyloxy group, C₆₋₁₀ aryloxy group, C₇₋₁₉ aralkyloxy group, mercapto group, mercapto c₁₋₆ alkyl group, sulfo group, sulfo C₁₋₆ alkyl group, C₁₋₆ alkylthio group, C₁₋₆ alkylthio C₁₋₆ alkyl group, C₃₋₁₀ cycloalkylthio group, C₆₋₁₀ arylthio group, C₇₋₁₉ aralkylthio group, amino group, amino C₁₋₆ alkyl group, mono-C₁₋₆ alkylamino group, di-C₁₋₆ alkylamino group, mono-C₁₋₆ alkylamino C₁₋₆ alkyl group, di-C₁₋₆ alkylamino C₁₋₆ alkyl group, C₃₋₁₀ cycloalkylamino group, C₆₋₁₀ arylamino group, C₇₋₁₉ aralkylamino group, cyclic amino group, cyclic amino C₁₋₆ alkyl group, cyclic amino C₁₋₆ alkylamino group, azido group, nitro group, halogen atom, halogeno C₁₋₆ alkyl group, cyano group, cyano C₁₋₆ alkyl group, carboxyl group, carboxy C₁₋₆ alkyl group, C₁₋₁₀ alkoxy-carbonyl group, C₁₋₁₀ alkoxy-carbonyl C₁₋₆ alkyl group, C₆₋₁₀ aryloxy-carbonyl group, C₇₋₁₉ aralkyloxycarbonyl group, benzoyl, naphthoyl, phthaloyl, phenylacetyl, C₁₋₆ alkanoyl group, C₂₋₆ alkanoyl C₁₋₆ alkyl group, C₃₋₅ alkenoyl group, benzoyloxy, naphthoyloxy, phenylacetoxy, C₂₋₆ alkanoyloxy group, C₂₋₆ alkanoyloxy C₁₋₆ alkyl group, C₃₋₅ alkenoyloxy group, carbamoyl C₁₋₆ alkyl group, carbamoyl, N-methylcarbamoyl, N,N-dimethylcarbamoyl, N-ethylcarbamoyl, N,N-diethylcarbamoyl, N-phenylcarbamoyl, N-acetylcarbamoyl, N-Benzoylcarbamoyl, N-(p-methoxyphenyl)carbamoyl, thiocarbamoyl, N-methylthiocarbamoyl, N-Phenylthiocarbamoyl, carbamoyloxy, N-methylcarbamoyloxy, N,N-dimethylcarbamoyloxy, N-ethylcarbamoyloxy, N-phenylcarbamoyloxy, carbamoyloxy C₁₋₆ alkyl group, C₁₋₆ alkanoylamino group, benzamido, naphthoylamido, phthalimido, sulfonamido group, carboxyamino group, C₁₋₁₀ alkoxycarboxamido group, C₆₋₁₀ aryloxy-carboxamido group, and C₇₋₁₉ aralkyloxy-carboxamido group, or a physiologically or pharmaceutically acceptable salt or ester thereof, (the compound (I), and pharmaceutically acceptable salt and ester thereof may simply be abbreviated hereinafter as the compound (I) or the antibacterial compound (I)). More specifically, the antibacterial compounds of the present invention are cephem compounds represented by the formula (I) (Z=S, S → O) as well as oxa-(Z=O) or carba-(Z=CH₂) derivatives thereof. The cephem compounds in the present specification are a group of compounds named on the basis of "cepham" disclosed in "The Journal of the American Chemical Society" Vol. 84, p. 3400 (1962), and mean, among the cepham compounds, those having a double bond at the 3,4-position. As stated hereinbefore, it has gradually become apparent that a cephem compound as well as oxa- or carba-derivatives thereof having a quaternary ammoniomethyl group at the 3-position and an aminothiazolyloxyiminoacetamido group or nitrogen containing heterocycle-amino group at the 7-position simultaneously has especially excellent antibacterial activity and specific antibacterial spectrum. A number of compounds having a nitrogen-containing aromatic heterocyclic ring as the quaternary ammoniomethyl group at the 3-position have already been synthesized and corresponding patent applications have been published. Most of those heterocyclic rings are monocyclic pyridinium groups or those having a substituent on the ring thereof, and compounds of this invention having an imidazolium-1-yl group which forms a condensed ring at the 2,3-position or the 3,4-position have not been synthesized at all. The present inventors succeeded in synthesizing the compounds represented by the formula (I) having such structural features, and examined the antibacterial activities and antibacterial spectrum, resulting in the findings that the compounds (I) or their pharmaceutically acceptable salts or esters have strong antibacterial action against various bacteria, especially against cephalosporin-resistant bacteria, and that they show specific antibacterial action against bacteria belonging to the genus Pseudomonas , and completed the present invention. Reference is made as follows to the group names and symbols used in the present specification. Unless otherwise specifically defined, those groups and symbols are of the following meanings respectively. "C₁₋₆ Alkyl group" is preferably a straight-chain or branched lower alkyl group having 1-6 carbon atoms (hereinafter sometimes mentioned briefly as "C₁₋₆ alkyl group"), which is exemplified by methyl, ethyl, n-propyl, isopropyl, n-butyl, isobutyl, sec-butyl, tert-butyl, n-pentyl or n-hexyl. "C₂₋₆ Alkenyl group" is preferably a straight-chain or branched lower alkenyl group having 2-6 carbon atoms (hereinafter sometimes mentioned briefly as "C₂₋₆ alkenyl group"), which is exemplified by vinyl, allyl, 1-propenyl, isopropenyl, 1-butenyl, 2-butenyl, 3-butenyl, methallyl or 1,1-dimethylallyl. "C₂₋₆ Alkynyl group" is preferably a straight-chain or branched lower alkynyl group having 2-6 carbon atoms (hereinafter sometimes mentioned briefly as "C₂₋₆ alkynyl group"), which is exemplified by ethynyl, 1-propynyl or propargyl. "C₃₋₁₀ Cycloalkyl group" is preferably a 3-7 membered alicyclic hydrocarbon group having 3-10 carbon atoms (hereinafter sometimes mentioned briefly as "C₃₋₁₀ cycloalkyl group"), which is exemplified by cyclopropyl, cyclobutyl, cyclopentyl, cyclohexyl, cycloheptyl, norbornyl or adamantyl. "C₅₋₆ Cycloalkenyl group" is preferably a 5-6 membered alicyclic hydrocarbon group having one or two double bonds (hereinafter sometimes mentioned briefly as C₅₋₆ cycloalkenyl group"), which is exemplified by cyclopentenyl, cyclopentadienyl, cyclohexenyl or cyclohexadienyl. "C₆₋₁₀ Aryl group" is preferably an aromatic hydrocarbon group having 6-10 carbon atoms (hereinafter sometimes mentioned briefly as "C₆₋₁₀ aryl group"), which is exemplified by phenyl, alpha-naphthyl, β-naphthyl or biphenylyl. "C₇₋₁₉ Aralkyl group" is preferably an aromatically substituted alkyl group having 7-12 carbon atoms (hereinafter sometimes mentioned briefly as "C₇₋₁₂ aralkyl group"), which is exemplified by benzyl, 1-phenylethyl, 2-phenylethyl, phenylpropyl or naphthylmethyl. Incidentally, the C₇₋₁₂ aralkyl group, in combination with the di-C₆₋₁₀ aryl-methyl group and tri-c₆₋₁₀ aryl-methyl group, is sometimes stated as "C₇₋₁₉-aralkyl group". "Di-C₆₋₁₀ arylmethyl group" means methyl group substituted with two C₆₋₁₀ aryl groups mentioned above (hereinafter sometimes mentioned briefly as "di-C₆₋₁₀ aryl-methyl group"), which is exemplified by benzhydryl. "Tri-C₆₋₁₀ arylmethyl group" means methyl group substituted with three C₆₋₁₀ aryl groups mentioned above (hereinafter sometimes mentioned briefly as "tri-C₆₋₁₀ aryl-methyl group"), which is exemplified by trityl. The C₆₋₁₀ aryl group of "C₆₋₁₀ arylmethylene group" is preferably a C₆₋₁₀ aryl group mentioned above, hence "arylmethylene group" is hereinafter sometimes called "C₆₋₁₀ aryl-methylene group", which is exemplified by benzylidene (C₆H₅CH=). The C₁₋₆ alkyl group of the "C₁₋₆ alkoxy group" is preferably a C₁₋₆ alkyl group mentioned above, which is exemplified by methoxy, ethoxy, n-propoxy, isopropoxy, n-butoxy, tert-butoxy, amyloxy or hexyloxy. The C₃₋₁₀ cycloalkyl group of "C₃₋₁₀ cycloalkyloxy group" is preferably a C₃₋₁₀ cycloalkyl group mentioned above, which is exemplified by cyclopropyloxy, cyclopentyloxy, cyclohexyloxy or norbornyloxy. The C₆₋₁₀ aryl group of "C₆₋₁₀ aryloxy group" is preferably a C₆₋₁₀ aryl group mentioned above, which is exemplified by phenoxy or naphthyloxy. The C₇₋₁₉ aralkyl group of "C₇₋₁₉ aralkyloxy group" is preferably a C₇₋₁₉ aralkyl group mentioned above, which is exemplified by benzyloxy, 1-phenylethyloxy, 2-phenylethyloxy, naphthylmethyloxy, benzhydryloxy or trityloxy. The C₁₋₆ alkyl group of "C₁₋₆ alkylthio group" is preferably a C₁₋₆ alkyl group mentioned above, which is exemplified by methylthio, ethyltio, n-propylthio or n-butylthio. The C₁₋₆ alkylthio group of "amino C₁₋₆ alkylthio group" is preferably a C₁₋₆ alkylthio group mentioned above, hence "aminoalkylthio group" is hereinafter called "amino C₁₋₆ alkylthio group", which is exemplified by aminomethylthio, 2-aminoethylthio or 3-aminopropylthio. The C₂₋₆ alkenyl group of "C₂₋₆ alkenylthio group" is preferably a C₂₋₆ alkenyl group mentioned above, hence "alkenylthio group" is hereinafter sometimes called "C₂₋₆ alkenylthio group", which is exemplified by vinylthio, allylthio, 1-propenylthio or isopropenylthio. The C₃₋₁₀ cycloalkyl group of "C₃₋₁₀ cycloalkylthio group" is preferably a C₃₋₁₀ cycloalkyl group mentioned above, which is exemplified by cyclopropylthio or cyclohexylthio. The C₆₋₁₀ aryl group of the "C₆₋₁₀ arylthio group" is preferably C₆₋₁₀ aryl group mentioned above, which is exemplified by phenylthio or naphthylthio. The C₇₋₁₉ aralkyl group of "C₇₋₁₉ aralkylthio group" is preferably a C₇₋₁₉ aralkyl group mentioned above, which is exemplified by benzylthio, phenylethylthio, benzhydrylthio or tritylthio. The C₁₋₆ alkyl group of "mono-C₁₋₆ alkylamino group" is preferably a C₁₋₆ alkyl group mentioned above, which is exemplified by methylamino, ethylamino, n-propylamino, n-butylamino, tert-butylamino, n-pentylamino or n-hexylamino. The C₁₋₆ alkyl group of "di-C₁₋₆ alkylamino group" is preferably C₁₋₆ alkyl group mentioned above, which is exemplified by dimethylamino, diethylamino, methylethylamino, di-(n-propyl)amino or di-(n-butyl)amino. The C₁₋₆ alkyl group of "tri-C₁₋₆ alkylammonium group" is preferably a C₁₋₆ alkyl group mentioned above, which is exemplified by trimethylammonium [(CH₃)₃N⁺-] or triethylammonium. The trialkylammonium group is usually accompanied by a corresponding anion exemplified by a halogenide ion (chloride ion, bromide ion, iodide ion, etc.), sulfate ion, nitrate ion, carbonate ion, organic carboxylate ion (e.g. oxalate ion or trifluoroacetate ion), organic sulfonate ion (e.g. methanesulfonate ion or p-toluenesulfonate ion). The organic carboxylate ion and the organic sulfonate ion may sometimes be intramolecular ones. The C₃₋₁₀ cycloalkyl group of "C₃₋₁₀ cycloalkylamino group" is preferably C₃₋₁₀ cycloalkyl group mentioned above, which is exemplified by cyclopropylamino, cyclopentylamino or cyclohexylamino. The C₆₋₁₀ aryl group of "C₆₋₁₀ arylamino group" is preferably a C₆₋₁₀ aryl group mentioned above, which is exemplified by anilino or N-methylanilino. The C₇₋₁₉ aralkyl group of "C₇₋₁₉ aralkylamino group" is preferably a C₇₋₁₉ aralkyl group mentioned above, which is exemplified by benzylamino, 1-phenylethylamino, 2-phenylethylamino, benzhydrylamino or tritylamino. "Cyclic amino group" means a group formed by removing one of the hydrogen atoms attached to the ring-constituting nitrogen atom of a nitrogen-containing heterocyclic ring as described hereafter, which is exemplified by 1H-tetrazol-1-yl, 1H-pyrrol-1-yl, pyrrolino, pyrrolidino, 1H-imidazol-1-yl, imidazolino, imidazolidino, 1H-pyrazol-1-yl, pyrazolino, pyrazolidino, piperidino, piperazino or morpholino. The C₁₋₆ alkyl group of the "hydroxy C₁₋₆ alkyl group" is preferably a C₁₋₆ alkyl group mentioned above, which is exemplified by hydroxymethyl, 1-hydroxyethyl, 2-hydroxyethyl or 3-hydroxypropyl. The C₁₋₆ alkyl group of "C₁₋₆ mercapto C₁₋₆ alkyl group" is preferably a C₁₋₆ alkyl group mentioned above, which is exemplified by mercaptomethyl, 1-mercaptoethyl or 2-mercaptoethyl. The C₁₋₆ alkoxy group of "C₁₋₆ alkoxy C₁₋₆ alkyl group" is preferably a C₁₋₆ alkoxy group mentioned above and the C₁₋₆ alkyl group of "C₁₋₆ alkoxy C₁₋₆ alkyl group" is preferably a C₁₋₆ alkyl group mentioned above, which is exemplified by methoxymethyl, ethoxymethyl or 2-methoxyethyl. The C₁₋₆ alkylthio group of "C₁₋₆ alkylthio C₁₋₆ alkyl group" is preferably C₁₋₆ alkylthio group mentioned above and the C₁₋₆ alkyl group of "C₁₋₆ alkylthio C₁₋₆ alkyl group" is preferably a C₁₋₆ alkyl group mentioned above, which is exemplified by methylthiomethyl or 2-methylthioethyl. The C₁₋₆ alkyl group of "amino C₁₋₆ alkyl group" is preferably a C₁₋₆ alkyl group mentioned above, which is exemplified by aminomethyl, 2-aminoethyl or 3-aminopropyl. "Mono C₁₋₆ alkylamino C₁₋₆ alkyl group" is preferably a "mono-C₁₋₆ alkyl amino C₁₋₆ alkyl group", which is exemplified by methylaminomethyl, ethylaminomethyl, 2-(N-methylamino)ethyl or 3-(N-methylamino)propyl. "Di C₁₋₆ alkylamino C₁₋₆ alkyl group" is preferably a "di-C₁₋₆ alkylamino C₁₋₆ alkyl group", which is exemplified by N,N-dimethylaminomethyl, N,N-diethylaminomethyl, 2-(N,N-dimethylamino)ethyl, 2-(N,N-diethylamino)ethyl or 3-(N,N-diethylamino)propyl. The cyclic amino group of "cyclic amino C₁₋₆ alkyl group" is preferably the one mentioned above and the C₁₋₆ alkyl group of "cyclic amino C₁₋₆ alkyl group" is preferably a C₁₋₆ alkyl group mentioned above, which is exemplified by pyrrolidinomethyl, piperidinomethyl, piperazinomethyl, morpholinomethyl or 2-(morpholino)ethyl. The cyclic amino C₁₋₆ alkyl group of "cyclic amino C₁₋₆ alkylamino group" is preferably cyclic amino C₁₋₆ alkyl group mentioned above, which is exemplified by pyrrolidinomethylamino, piperizinomethylamino, piperazinomethylamino or morpholinomethylamino. The C₁₋₆ alkyl group of "halogeno C₁₋₆ alkyl group" is preferably a C₁₋₆ alkyl group mentioned above, which is exemplified by fluoromethyl, difluoromethyl, trifluoromethyl, chloromethyl, dichloromethyl, trichloromethyl, 2-fluoroethyl, 2,2-difluoroethyl, 2,2,2-trifluoroethyl, 2-chloroethyl, 2,2-dichloroethyl, 2,2,2-trichloroethyl, 2-bromoethyl, or 2-iodoethyl. The C₁₋₆ alkyl group of "cyano C₁₋₆ alkyl group" is preferably a C₁₋₆ alkyl group mentioned above, which is exemplified by cyanomethyl or 2-cyanoethyl. The C₁₋₆ alkyl group of "carboxy C₁₋₆ alkyl group" is preferably a C₁₋₆ alkyl group mentioned above, which is exemplified by carboxymethyl, 1-carboxyethyl or 2-carboxyethyl. The C₁₋₆ alkyl group of "sulfo C₁₋₆ alkyl group" is preferably a C₁₋₆ alkyl group mentioned above, which is exemplified by sulfomethyl or 2-sulfoethyl. The C₂₋₆ alkanoyl group of "C₂₋₆ alkanoyl C₁₋₆ alkyl group is preferably a C₂₋₆ alkanoyl group mentioned hereafter and the C₁₋₆ alkyl group of "C₂₋₆ alkanoyl C₁₋₆ alkyl group" is preferably a C₁₋₆ alkyl group mentioned above, which is exemplified by acetylmethyl, 1-acetylethyl or 2-acetylethyl. The C₂₋₆ alkanoyloxy group of the "C₂₋₆ alkanoyloxy C₁₋₆ alkyl group" is preferably a C₂₋₆ alkanoyloxy group to be described hereafter and the C₁₋₆ alkyl group of "C₂₋₅ alkanoyloxy C₁₋₆ alkyl group is preferably a C₁₋₆ alkyl group mentioned above, which is exemplified by acetoxymethyl, 1-acetoxyethyl or 2-acetoxyethyl. The C₁₋₁₀ alkoxycarbonyl group of "C₁₋₁₀ alkoxycarbonyl C₁₋₆ alkyl group" is preferably a C₁₋₁₀ alkoxy-carbonyl group to be described hereinafter and the C₁₋₆ alkyl group of "C₁₋₁₀ alkoxycarbonyl C₁₋₆ alkyl group" is preferably C₁₋₆ alkyl group mentioned above, which is exemplified by methoxycarbonylmethyl, ethoxycarbonylmethyl or tert-butoxycarbonylmethyl. The C₁₋₆ alkyl group of "carbamoyl C₁₋₆ alkyl group" is preferably C₁₋₆ alkyl group, which is exemplified by carbamoylmethyl. The C₁₋₆ alkyl group of "carbamoyloxy C₁₋₆ alkyl group" is preferably a C₁₋₆ alkyl group, which is exemplified by carbamoyloxymethyl. "Halogen atom" is exemplified by fluorine, chlorine, bromine or iodine. "C₁₋₆ Alkanoyl group" is preferably an aliphatic acyl group having 1-6 carbon atoms (hereinafter sometimes called simply "C₁₋₆ alkanoyl group"), which is exemplified by formyl, acetyl, propionyl, butyryl, isobutyryl, valeryl, isovaleryl or pivaloyl. These alkanoyl groups, except formyl, are sometimes called "C₂₋₆ alkanoyl group". "C₃₋₅ Alkenoyl group" is preferably one having 3-5 carbon atoms (hereinafter sometimes simply called "C₃₋₅ alkenoyl group"), which is exemplified by acryloyl, crotonoyl or maleoyl. The C₃₋₁₀ cycloalkyl group of "C₃₋₁₀ cycloalkylcarbonyl group" is preferably a C₃₋₁₀ cycloalkyl group mentioned above, which is exemplified by cyclopropylcarbonyl, cyclobutylcarbonyl, cyclopentylcarbonyl, cyclohexylcarbonyl, cycloheptylcarbonyl or adamantylcarbonyl. The C₅₋₆ cycloalkenyl group of "C₅₋₆ cycloalkenylcarbonyl group" is preferably a C₅₋₆ cycloalkenyl group, which is exemplified by cyclopentenylcarbonyl, cyclopentadienylcarbonyl, cyclohexenylcarbonyl or cyclohexadienylcarbonyl. The C₆₋₁₀ aryl group of "C₆₋₁₀ arylcarbonyl group" is preferably a C₆₋₁₀ aryl group mentioned above, which is exemplified by benzoyl or naphthoyl. The C₇₋₁₉ aralkyl group of "C₇₋₁₉ aralkylcarbonyl group" is preferably a C₇₋₁₉ aralkyl group, which is exemplified by phenylacetyl, phenylpropionyl, alpha,alpha-diphenylacetyl or alpha,alpha,alpha-triphenylacetyl. The C₁₋₁₀ alkyl group of "C₁₋₁₀ alkoxycarbonyl group" includes in this specification, a C₃₋₁₀ cycloalkyl group mentioned above, besides lower alkyl groups having 1-8 carbon atoms, which is exemplified by methoxycarbonyl, ethoxycarbonyl, n-propoxycarbonyl, isopropoxycarbonyl, n-butoxycarbonyl, isobutoxycarbonyl, tert-butoxycarbonyl, cyclopentyloxycarbonyl, cyclohexyloxycarbonyl or norbornyloxycarbonyl. The C₆₋₁₀ aryloxy group of "C₆₋₁₀ aryloxycarbonyl group" is preferably a C₆₋₁₀ aryloxy group mentioned above, which is exemplified by phenoxycarbonyl or naphthyloxycarbonyl. The C₇₋₁₉ aralkyloxy group of "C₇₋₁₉ aralkyloxycarbonyl group" is preferably a C₇₋₁₉ aralkyloxy group mentioned above, which is exemplified by benzyloxycarbonyl, benzhydryloxycarbonyl or trityloxycarbonyl. The C₁₋₆ alkylthio group of "C₁₋₆ alkylthio-carbonyl group" is preferably C₁₋₆ alkylthio group mentioned above, which is exemplified by methylthiocarbonyl, ethylthiocarbonyl, n-propylthiocarbonyl or n-butylthiocarbonyl. The C₁₋₆ alkanoyl group of "C₁₋₆ alkanoyloxy group" is preferably a C₁₋₆ alkanoyl group mentioned above, which is exemplified by formyloxy, acetoxy, propionyloxy, butyryloxy, valeryloxy or pivaloyloxy. These alkanoyloxy groups, except formyloxy, are sometimes called "C₂₋₆ alkanoyloxy group". The C₃₋₅ alkenoyl group of "C₃₋₅ alkenoyloxy group" is preferably a C₃₋₅ alkenoyl group mentioned above, which is exemplified by acryloyloxy or crotonoyloxy. The C₁₋₆ alkyl group of "mono C₁₋₆ alkylcarbamoyl group" is preferably a C₁₋₆ alkyl group mentioned above, which is exemplified by N-methylcarbamoyl or N-ethylcarbamoyl. The C₁₋₆ alkyl group of "C₁₋₆ dialkylcarbamoyl group" is preferably a C₁₋₆ alkyl group, which is exemplified by N,N-dimethylcarbamoyl or N,N-diethylcarbamoyl. The mono C₁₋₆ alkylcarbamoyl group of "mono C₁₋₆ alkylcarbamoyloxy group" is preferably mono-C₁₋₆ alkylcarbamoyl group mentioned above, which is exemplified by N-methylcarbamoyloxy or N-ethylcarbamoyloxy. The di C₁₋₆ alkylcarbamoyl group of the "di C₁₋₆ alkylcarbamoyloxy group" is preferably a di-C₁₋₆ alkylcarbamoyl group mentioned above, which is exemplified by N,N-dimethylcarbamoyloxy or N,N-diethylcarbamoyloxy. The C₁₋₆ alkyl group of "C₁₋₆ alkylsulfonyl group" is preferably a C₁₋₆ alkyl group mentioned above, which is exemplified by methanesulfonyl or ethanesulfonyl. The C₆₋₁₀ aryl group of "C₆₋₁₀ arylsulfonyl group" is preferably a C₆₋₁₀ aryl group mentioned above, which is exemplified by, among others, benzenesulfonyl. The C₇₋₁₉ aralkyl group of "C₇₋₁₉ aralkylsulfonyl group" is preferably a C₇₋₁₉ aralkyl group mentioned above, which is exemplified by phenylmethanesulfonyl or diphenylmethanesulfonyl. The C₁₋₆ alkylsulfonyl group of "C₁₋₆ alkylsulfonyl group" is preferably a C₁₋₆ alkylsulfonyl group mentioned above, which is exemplified by methanesulfonyloxy or ethanesulfonyloxy. The C₆₋₁₀ arylsulfonyl group of "C₆₋₁₀ arylsulfonyloxy group" is preferably a C₆₋₁₀ arylsulfonyl group, which is exemplified by, among others, benzenesulfonyloxy. The C₇₋₁₉ aralkylsulfonyl group of "C₇₋₁₉ aralkylsulfonyloxy group" is preferably a C₇₋₁₉ aralkylsulfonyl group mentioned above, which is exemplified by phenylmethanesulfonyloxy or diphenylmethanesulfonyloxy. "Amino acid residue" means acyl groups formed by removing hydroxyl group of the carboxyl group of conventional amino acids, which is exemplified by glycyl, alanyl, valyl, leucyl, isoleucyl, seryl, threonyl, cysteinyl, cystinyl, methionyl, aspartyl, glutamyl, lysyl, arginyl, phenylglycyl, phenylalanyl, tyrosyl, histidyl, triptophanyl or prolyl. "5 to 8-membered ring containing one to four heteroatoms of nitrogen which may optionally be oxidized" means 5 to 8 membered ring containing 1 to 4 nitrogen atoms (optionally oxidized) or condensed ring thereof, which may contain, besides nitrogen atoms, one to several, preferably 1 to 2 hetero atoms such as oxygen atom or sulfur atom. "5 to 8-membered ring group" means a group formed by removing one hydrogen atom bonding to ring-forming carbon atom of the above 5 to 8-membered ring containing one to four heteroatoms of nitrogen which may optionally be oxidized. "Heterocyclic group" means a group formed by removing one hydrogen atom bonding to a carbon atom of a heterocyclic ring, which means 5 to 8 membered ring containing one to several, preferably 1 to 4 hetero atoms such as nitrogen atom (optionally oxidized), oxygen atom or sulfur atom, or condensed ring thereof, which is exemplified by 2- or 3-pyrrolyl, 3-, 4- or 5-pyrazolyl, 2-, 4- or 5-imidazolyl, 1,2,3- or 1,2,4-triazolyl, 1H- or 2H-tetrazolyl, 2- or 3-furyl, 2- or 3-thienyl, 2-, 4- or 5-oxazolyl, 3-, 4- or 5-isoxazolyl, 1,2,3-oxadiazol-4- or 5-yl, 1,2,4-oxadiazol-3- or 5-yl, 1,2,5- or 1,3,4-oxadiazolyl, 2-, 4- or 5-thiazolyl, 3-, 4- or 5-isothiazolyl, 1,2,3-thiadiazol-4- or 5-yl, 1,2,4-thiadiazol-3- or 5-yl, 1,2,5- or 1,3,4-thiadiazolyl, 2- or 3-pyrrolidinyl, 2-, 3- or 4-pyridyl, 2-, 3- or 4-pyridyl-N-oxide, 3- or 4-pyridazinyl, 3- or 4-pyridazinyl-N-oxide, 2-, 4- or 5-pyrimidinyl, 2-, 4- or 5-pyrimidinyl-N-oxide, pyrazinyl, 2-, 3- or 4-piparidinyl, piperazinyl, 3H-indol-2- or 3-yl, 2-, 3- or 4-pyranyl, 2-, 3- or 4-thiopyranyl, benzopyranyl, quinolyl, pyrido[2,3-d]pyrimidyl, 1,5-, 1,6-, 1,7-, 1,8- 2,6- or 2,7-naphthylidyl, thieno[2,3-d]-pyridyl, pyrimidopyrimidyl, pyrazinoquinolyl, or benzopyranyl. Heterocyclic groups of "heterocycle-oxy group", "heterocycle-thio group", "heterocycle-amino group", "heterocycle-carbonyl group", "heterocycle-acetyl group" and "heterocycle-carboxamido group" are all preferably "heterocyclic goup" mentioned above. "Quaternary ammonium group" means a group in which the bonding hand is the unpaired electron located on one of the tertiary nitrogen atoms of the above-mentioned nitrogen-containing heterocyclic ring, and per se quaternarized, necessarily being accompanied with corresponding anion. The quaternary ammonium group is exemplified by oxazolium, thiazolium, isoxazolium, isothiazolium, pyridinium or quinolinium. The anion is exemplified by hydroxide ion, halogenide ion (e.g. chloride ion, bromide ion or iodide ion), sulfate ion, nitrate ion, carbonate ion, organic carboxylate ion (e.g. oxalate ion or trifluoroacetate ion) or organic sulfonate ion (e.g. p-toluenesulfonate ion), the latter two being sometimes intramolecular ones. The groups bearing asterisk* at the right shoulder are "optionally substituted groups" For example, alkyl* group means "optionally substituted alkyl group". The number of substituents is not restricted to one, but two to four, preferably 2 to 3, which may be the same or different. "C₆₋₁₀ aryl* group", c₇₋₁₂ aralkyl* group, C₆₋₁₀ aryl*oxy group" and "C₇₋₁₉ aralkyl*oxy group" are preferably "phenyl* group", "benzyl* group", "phenoxy* group" and "benzyl*oxy group", respectively. The substituents of "optionally substituted C₁₋₆ alkanoyl group" represented by C₁₋₆ alkanoyl* group are exemplified by (1) heterocycle*carbonyl group in case of C₁ alkanoyl (i.e. formyl) and (2) "substituent S¹" described below in case of C₂₋₆ alkanoyl group (i.e. acetyl, propionyl, butyryl, isobutyryl, valeryl, isovaleryl, pivaloyl etc). The "substituent S¹" is exemplified by C₃₋₁₀ cycloalkyl* group, C₅₋₆ cycloalkenyl* group, C₆₋₁₀ aryl* group, hydroxyl group, C₁₋₆ alkoxy group, C₃₋₁₀cycloalkyloxy group, C₆₋₁₀ aryl*oxy group, C₇₋₁₉ aralkyl*oxy group, mercapto group, C₁₋₆ alkyl*thio group, amino C₁₋₆ alkylthio group, C₂₋₆ alkenyl*thio group, c₃₋₁₀ cycloalkylthio group, C₆₋₁₀ aryl*thio group, C₇₋₁₉ aralkyl*thio group, amino group, mono-C₁₋₆alkylamino group, di-C₁₋₆ alkylamino group, C₃₋₁₀ cycloalkylamino group, C₆₋₁₀ aryl*amino group, c₇₋₁₉ aralkyl*amino group, cyclic amino* group, halogen atom, nitro group, azido group, cyano group, carboxyl group, acyl⁺ group, substituted oxycarbonyl group, C₁₋₆ alkylthio-carbonyl group, acyl⁺oxy group, acyl⁺amino group, acyl⁺aminoalkylthio group, carbamoyl group, mono-C₁₋₆ alkylcarbamoyl group, di-C₁₋₆ alkyl carbamoyl group, carbamoyloxy group, mono-C₁₋₆ alkylcarbamoyloxy group, di-C₁₋₆ alkylcarbamoyloxy group, sulfo group, hydroxysulfonyloxy group, C₁₋₆ alkylsulfonyl group, C₆₋₁₀ aryl*sulfonyl group, C₇₋₁₉ aralkyl*sulfonyl group, c₁₋₆ alkylsulfonyloxy group, C₆₋₁₀ aryl*sulfonyloxy group, C₇₋₁₉ aralkyl*sulfonyloxy group, ureido* group, sulfamoyl* group, heterocyclic* group, heterocycle* oxy group, heterocycle*thio group, heterocycle*amino group, heterocycle*carbonyl group, heterocycle*carboxamido group or quaternary ammonium* group. The number of these substituents is not restricted to one. But it is preferably one to four. In case there are two or more substituents, these substituents may be the same or different. To state further, two of these substituents may be combined to form C=C double bond or C=N double bond as described below. The substituents (hereinafter referred to as "substituents S²") of "optionally substituted C₃₋₅ alkenoyl group" are exemplified by C₃₋₁₀ cycloalkyl group, C₆₋₁₀ aryl* group, C₁₋₆ alkoxy group, C₆₋₁₀ aryl*oxy group, C₇₋₁₉ aralkyl*oxy group, halogen atom, cyano group, carboxyl group, acyl⁺ group, substituted oxycarbonyl group, acyl⁺oxy group, heterocyclic* group or quaternary ammonium* group. The substituents of "optionally substituted C₆₋₁₀ aryl-carbonyl group" represented by C₆₋₁₀ aryl* carbonyl group as well as "optionally substituted heterocyclic group" represented by heterocycle* carbonyl group (hereinafter collectively referred to as "substituent S³" are exemplified by C₁₋₆ alkyl group, C₂₋₆ alkenyl group, C₆₋₁₀ aryl group, C₇₋₁₂ aralkyl group, di-C₆₋₁₀ aryl-methyl group, tri-C₆₋₁₀ aryl-methyl group, hydroxyl group, C₁₋₆ alkoxy group, C₆₋₁₀ aryloxy group, C₇₋₁₉ aralkyloxy group, mercapto group, C₁₋₆ alkylthio group, C₆₋₁₀ arylthio group, C₇₋₁₉ aralkylthio group, amino group, mono-C₁₋₆ alkylamino group, di-C₁₋₆ alkylamino group, hydroxy-C₁₋₆ alkyl group, mercapto C₁₋₆ alkyl group, halogeno C₁₋₆ alkyl group, carboxy C₁₋₆ alkyl group, halogen atom, nitro group, azido group, cyano group, carboxyl group, substituted oxycarbonyl group, acyl⁺ group, acyl⁺oxy group, acyl*amino group, carbamoyl group, thiocarbamoyl group, C₁₋₆ alkylsulfonyl group, C₆₋₁₀ arylsulfonyl group or C₇₋₁₉ aralkylsulfonyl group. Among the above-mentioned substituents (S¹, S² and S³) of C₁₋₆ alkanoyl group, C₃₋₅ alkenoyl group, C₆₋₁₀ aryl-carbonyl group and heterocycle*carbonyl group, those which are not described below are of the same meaning as afore-mentioned. The substituents of the C₆₋₁₀ aryl group of C₆₋₁₀ aryl* group, phenyl* group, C₆₋₁₀ aryl*oxy group, phenoxy* group, C₆₋₁₀ aryl*thio group, C₆₋₁₀ aryl*amino group, C₆₋₁₀ aryl*sulfonyl group and C₆₋₁₀ aryl*sulfonyloxy group are also named here by the above-mentioned substituents S³. The substituents of the aromatic ring of the C₇₋₁₂ or C₇₋₁₉ aralkyl groups of C₇₋₁₂ aralkyl* group, benzyl* group, C₇₋₁₉ aralkyl*oxy group, benzyl*oxy group, C₇₋₁₉ aralkyl*thio group, C₇₋₁₉ aralkyl*amino group, C₇₋₁₉ aralkyl*sulfonyl group and C₇₋₁₉ aralkyl*sulfonyloxy group are also named here by the above-mentioned substituents S³. The substituents of the heterocyclic ring of the heterocyclic* group, heterocycle*oxy group, heterocycle*thio group, heterocycle*amino group, heterocycle*acetyl group and heterocycle*carboxamido group are also named here by the above-mentioned substituents S³. The substituents on the nitrogen-containing heterocyclic ring of quaternary ammonium* group are also named here by the above mentioned substituents S³. The substituents of the C₁₋₆ alkyl group of "optionally substituted C₁₋₆ alkyl group" representable by C₁₋₆ alkyl* group are also named here by the above-mentioned substituents S¹. The substituents of the "optionally substituted C₃₋₁₀ cycloalkyl group" and "optionally substituted C₅₋₆ cycloalkenyl group" representable by C₃₋₁₀ cycloalkyl group and C₅₋₆ cycloalkenyl* group are also named here by the above-mentioned substituents S³. The substituents of the C₁₋₆ alkylthio groups of "optionally substituted C₁₋₆ alkylthio group" representable by C₁₋₆ alkyl*thio group (These substitutents are hereinafter referred to as "substituent S⁴") are exemplified by hydroxyl group, C₁₋₆ alkoxy group, C₃₋₁₀ cycloalkyloxy group, C₆₋₁₀ aryl*oxy group, C₇₋₁₉ aralkyl*oxy group, mercapto group, C₁₋₆ alkylthio group, C₃₋₁₀ cycloalkylthio group, C₆₋₁₀ aryl*thio group, C₇₋₁₉ aralkyl*thio group, amino group, mono-C₁₋₆ alkylamino group, di-C₁₋₆ alkylamino group, cyclic amino* group, halogen atom, cyano group, carboxyl group, carbamoyl group, acyl⁺oxy group, sulfo group, or quaternary ammonium* group. The substituents of the C₂₋₆ alkenylthio group of "optionally substituted C₂₋₆ alkenylthio group" representable by C₂₋₆ alkenyl*thio group (these substituents are hereinafter referred to as "substituent S⁵") are exemplified by halogen atom, cyano group, carboxyl group, carbamoyl group, mono-C₁₋₆ alkylcarbamoyl group, di-C₁₋₆ alkylcarbamoyl group or thiocarbamoyl group. "Acyl⁺ group" means the above-mentioned C₁₋₆ alkanoyl group, C₆₋₁₀ aryl*carbonyl group, C₇₋₁₉ aralkyl*carbonyl group, heterocycle*carbonyl group or heterocycle*acetyl group. Representable acyl⁺ groups are exemplified by formyl, acetyl, propionyl, n-butyryl, isobutyryl, valeryl, pivaloyl, n-hexanoyl, chloroacetyl, dichloroacetyl, trichloroacetyl, 3-oxobutyryl, 4-chloro-3-oxobutyryl, 3-carboxypropionyl, 4-carboxybutyryl, 3-ethoxycarbamoylpropionyl, benzoyl, naphthoyl, p-methylbenzoyl, p-hydroxybenzoyl, p-methoxybenzoyl, p-chlorobenzoyl, p-nitrobenzoyl, o-carboxybenzoyl, o-(ethoxycarbonylcarbamoyl)benzoyl, o-(ethoxycarbonylsulfamoyl)benzoyl, phenylacetyl, p-methylphenylacetyl, p-hydroxyphenylacetyl, p-methoxyphenylacetyl, 2,2-diphenylacetyl, 2-thienylcarbonyl, 2-furylcarbonyl, 2-, 4- or 5-thiazolylacetyl, 2- or 3-thienylacetyl, 2- or 3-furylacetyl, 2-amino-4- or 5-thiazolylacetyl or 5-amino-3-thiadiazolylacetyl. The acyl⁺ group of "acyl⁺oxy group" and "acyl⁺amino group" means the above-mentioned acyl* group. Therefore, "acyl⁺oxy group" is exemplified by formyloxy, acetoxy, propionyloxy, butyryloxy, valeryloxy, pivaloyloxy, chloroacetoxy, dichloroacetoxy, trichloroacetoxy, 3-oxobutyryloxy, 4-chloro-3-oxobutyryloxy, 3-carboxypropionyloxy, 4-carboxybutyryloxy, 3-ethoxycarbamoylpropionyloxy, benzoyloxy, naphthoyloxy, p-methylbenzoyloxy, p-methoxybenzoyloxy, p-chlorobenzoyloxy, o-carboxybenzoyloxy, o-(ethoxycarbonylcarbamoyl)benzoyloxy, o-(ethoxycarbonylsulfamoyl)benzoyloxy, phenylacetyloxy, p-methylphenylacetyloxy, p-methoxyphenylacetyloxy, p-chlorophenylacetyloxy, 2,2-diphenylacetyloxy, thienylcarbonyloxy, furylcarbonyloxy, thiazolylacetyloxy, thienylacetyloxy or furylacetyloxy, and "acyl⁺amino group" is exemplified by acetamido (CH₃CONH-), benzamido (C₆H₅CONH-), phenylacetamido (C₆H₅CH₂CONH-) or 2-thienylacetamido The acyl*amino group and alkylthio group of "acyl⁺aminoalkylthio group" means respectively the above-mentioned acyl⁺amino group and C₁₋₆ alkylthio group, hence such "acyl⁺amino C₁₋₆ alkylthio group" being exemplified by acetamidomethylthio or 2-acetamidoethylthio. "Arylacyl⁺ group" is preferably "C₆₋₁₀ aryl-acyl⁺ group", which is exemplified by benzoyl, phthaloyl, naphthoyl or phenylacetyl. "Arylacyl⁺oxy group" is preferably "C₆₋₁₀ arylacy⁺oxy group", as exemplified by benzoyloxy, naphthoyloxy or phenylacetyloxy. The substituents of the ureido group of "optionally substituted ureido group" represented by "ureido* group" are exemplified by C₁₋₆ alkyl group, C₆₋₁₀ aryl* group, C₇₋₁₉ aralkyl* group, acyl⁺ group, carbamoyl group, sulfo group (which may form a salt with e.g. sodium or potassium), sulfamoyl group or amidino group. The substituents of the sulfamoyl group of "optionally substituted sulfamoyl group" represented by "sulfamoyl* group" are exemplified by C₁₋₆ alkyl group or amidino group. The substituents of "optionally substituted carbamoyl group" representable by "carbamoyl* group" and "carbamoyl*oxy group" are exemplified by C₁₋₆ alkyl group, C₆₋₁₀ aryl* group, C₇₋₁₂ aralkyl* group or acyl⁺ group, including the case where the nitrogen atom of carbamoyl group is the ring-forming nitrogen atom of the nitrogen-containing heterocyclic ring. The substituents of "optionally substituted thiocarbamoyl group" represented by "thiocarbamoyl* group" are exemplified by C₁₋₆ alkyl group, C₆₋₁₀ aryl* group, C₇₋₁₂ aralkyl* group or acyl⁺ group, including the case where the nitrogen atom of a thiocarbamoyl group is the ring-forming nitrogen atom of the nitrogen-containing heterocyclic ring. The substituents of the cyclic amino group of the "optionally substituted cyclic amino group" represented by "cyclic amino* group" (these substituents are hereinafter referred to as "substituent S⁶") are exemplified by C₁₋₆ alkyl group, C₂₋₆ alkenyl group, C₃₋₁₀ cycloalkyl group, C₆₋₁₀ aryl* group, C₇₋₁₂ aralkyl* group, di-C₆₋₁₀ aryl-methyl group, tri-C₆₋₁₀ aryl-methyl group, hydroxyl group, C₁₋₆ alkoxy group, C₆₋₁₀ aryl*oxy group, C₇₋₁₉ aralkyl*oxy group, mercapto group, C₁₋₆ alkylthio group, C₆₋₁₀ aryl*thio group, C₇₋₁₉ aralkyl*thio group, amino group, mono-C₁₋₆ alkylamino group, di-C₁₋₆ alkylamino group, C₆₋₁₀ aryl*amino group, C₇₋₁₉ aralkyl*amino group, halogen atom, nitro group, azido group, oxo group, thioxo group, cyano group, carboxyl group, acyl⁺ group, substituted oxycarbonyl group, acyl*oxy group, acyl⁺amino group, carbamoyl group, carbamoyloxy group, thiocarbamoyl group or sulfo group. The formyl group substituted with the heterocycle*carbonyl group mentioned above as one of the C₁₋₆ alkanoyl* groups is an acyl group having a formula of heterocycle*-CO-CO-, and the heterocyclic* group is also mentioned here as one exemplified above, but preferably, an optionally substituted oxazolyl group, thiazolyl group, oxadiazolyl group or thiadiazolyl group, for example. These heterocycle*-CO-CO- groups are exemplified by 2-(2-, 4- or 5-oxazolyl)-2-oxoacetyl, 2-(2-, 4- or 5-thiazolyl)-2-oxoacetyl, 2-(2-amino-4-thiazolyl)-2-oxoacetyl, 2-(1,2,4-oxadiazol-3- or 5-yl)-2-oxoacetyl, 2-(1,2,4-thiadiazol-3 or 5-yl)-2-oxoacetyl or 2-(5-amino-1,2,4-thiadiazol-3-yl)-2-oxoacetyl. The C₂₋₆ alkanoyl* group is most preferably a substituted acetyl group. The number of substituents of the substituted acetyl group is 1-3, and, as these substituents, "substituent S¹" mentioned above as substituents of C₁₋₆ alkanoyl groups are also mentioned here. When the number of substituents is 2-3, these substituents may be the same or different, and two of them may be combined to form a double bond. A detailed description about the subtituents R¹ and R³ follows. R¹ stands for an optionally protected amino group. In the field of synthesis of β-lactam and peptide, protecting groups of amino group have been sufficiently studied, and the methods of protection and deprotection have already been established. In the present invention as well, any of those known amino-protecting groups may suitably be employed. As such amino-protecting groups, there may be mentioned for example C₁₋₆ alkanoyl* group, C₃₋₅ alkenoyl* group, C₆₋₁₀ aryl*carbonyl group, phthaloyl group, heterocycle*carbonyl group, C₁₋₆ alkyl*sulfonyl group, camphorsulfonyl group, C₆₋₁₀ aryl*sulfonyl group, substituted oxycarbonyl group, carbamoyl* group, carbamoyloxy* group, thiocarbamoyl* group, C₆₋₁₀ aryl*methyl group, di-C₆₋₁₀ aryl*methyl group, tri-C₆₋₁₀ aryl*methyl group, C₆₋₁₀ aryl*methylene group, C₆₋₁₀ aryl*thio group, substituted silyl group or 2-C₁₋₁₀ alkoxycarbonyl-1-methyl-1-ethenyl group. As "C₁₋₆ alkanoyl* group", there may concretely be mentioned here formyl, acetyl, propionyl, butyryl, valeryl, pivaloyl, succinyl, glutaryl, monochloroacetyl, dichloroacetyl, trichloroacetyl, monobromoacetyl, monofluoroacetyl, difluoroacetyl, trifluoroacetyl, monoiodoacetyl, 3-oxobutyryl, 4-chloro-3-oxobutyryl, phenylacetyl, p-chlorophenylacetyl, phenoxyacetyl or p-chlorophenoxyacetyl. As "C₃₋₅ alkenoyl* group", there may concretely be mentioned here acryloyl, crotonoyl, maleoyl, cinnamoyl, p-chlorocinnamoyl or β-phenylcinnamoyl. As "C₆₋₁₀ aryl*carbonyl group", there may be mentioned, for example, benzoyl, naphtoyl, p-toluoyl, p-tert-butylbenzoyl, p-hydroxybenzoyl, p-methoxybenzoyl, p-tert-butoxybenzoyl, p-chlorobenzoyl or p-nitrobenzoyl. As the heterocycle*carbonyl group, there may be mentioned those as described hereinafter. As "C₁₋₆ alkyl*sulfonyl group", there may be mentioned, for example, methanesulfonyl or ethanesulfonyl. As "C₆₋₁₀ aryl*sulfonyl group", there may be mentioned here benzenesulfonyl, naphtalenesulfonyl, p-toluenesulfonyl, p-tert-butylbenzenesulfonyl, p-methoxybenzenesulfonyl, p-chlorobenzenesulfonyl or p-nitrobenzenesulfonyl, for example. "Substituted oxycarbonyl group" means not only the above-mentioned one, i.e. C₁₋₁₀ alkoxy-carbonyl group, C₆₋₁₀ aryloxycarbonyl group or C₇₋₁₉ aralkyloxycarbonyl group, but includes here one having substituents, and therefore there may be mentioned here methoxycarbonyl, ethoxycarbonyl, n-propoxycarbonyl, isopropoxycarbonyl, n-butoxycarbonyl, tert-butoxycarbonyl, cyclohexyloxycarbonyl, norbornyloxycarbonyl, phenoxycarbonyl, naphthyloxycarbonyl, benzyloxycarbonyl, methoxymethyloxycarbonyl, acetylmethyloxycarbonyl, 2-trimethylsilylethoxycarbonyl, 2-methanesulfonylethoxycarbonyl, 2,2,2-trichloroethoxycarbonyl, 2-cyanoethoxycarbonyl, p-methylphenoxycarbonyl, p-methoxyphenoxycarbonyl, p-chlorophenoxycarbonyl, p-methylbenzyloxycarbonyl, p-methoxybenzyloxycarbonyl, p-chlorobenzyloxycarbonyl, p-nitrobenzyloxycarbonyl, benzhydryloxycarbonyl, cyclopropyloxycarbonyl, cyclopentyloxycarbonyl or cyclohexyloxycarbonyl, for example. "Carbamoyl* group" is exemplified here by carbamoyl, N-methylcarbamoyl, N-ethylcarbamoyl, N,N-dimethylcarbamoyl, N,N-diethylcarbamoyl, N-phenylcarbamoyl, N-acetylcarbamoyl, N-benzoylcarbamoyl or N-(p-methoxyphenyl)carbamoyl. "Carbamoyl*oxy group" is exemplified here by carbamoyloxy, N-methylcarbamoyloxy, N,N-dimethylcarbamoyloxy, N-ethylcarbamoyloxy or N-phenylcarbamoyloxy. "Thiocarbamoyl* group" is exemplified here by thiocarbamoyl, N-methylthiocarbamoyl or N-phenylthiocarbamoyl, for example. "C₆₋₁₀ aryl*methyl group" is exemplified by benzyl, naphthylmethyl, p-methylbenzyl, p-methoxybenzyl, p-chlorobenzyl or p-nitrobenzyl. "Di-C₆₋₁₀ aryl*methyl group" is exemplified by benzhydryl or di-(p-tolyl)methyl. "Tri-C₆₋₁₀ aryl*methyl group" is exemplified by trityl or tri-(p-tolyl)methyl. "C₆₋₁₀ aryl*methylene group" is exemplified by benzylidene, p-methylbenzylidene or p-chlorobenzylidene. "C₆₋₁₀ aryl*thio group" is exemplified by o-nitrophenylthio. "Substituted silyl group" means a silyl group, together with the amino group to be protected, representable by the general formula: R⁶R⁷R⁸SiNH, (R⁶R⁷R⁸Si)₂N or (wherein R⁶, R⁷, R⁸, R⁹, R¹⁰, R 9' and R 10' are the same or different and stand for C₁₋₆ alkyl group or C₆₋₁₀ aryl* group, and Z' stands for C₁₋₃ alkylene group e.g. methylene, ethylene or propylene), which is exemplified by trimethylsilyl, tert-butyldimethylsilyl or -Si(CH₃)₂CH₂CH₂Si(CH₃)₂-. The C₁₋₁₀ alkoxy-carbonyl group of "2-C₁₋₁₀ alkoxycarbonyl1-methyl-1-ethenyl group" is preferably one of those mentioned in the foregoing. Hence, the 2-C₁₋₁₀ alkoxycarbonyl-1-methyl-1-ethenyl group is exemplified by 2-methoxycarbonyl-1-methyl-1-ethenyl, 2-ethoxycarbonyl-1-methyl-1-ethenyl, 2-tert-butoxycarbonyl-1-methyl-1-ethenyl, 2-cyclohexyloxycarbonyl-1-methyl-1-ethenyl or 2-norbornyloxycarbonyl-1-methyl-1-ethenyl. The symbol R³ stands for hydrogen atom or a substituted hydrocarbon residue. The hydrocarbon residue may be exemplified by a C₁₋₆ alkyl group, C₂₋₆ alkenyl group, C₂₋₆ alkynyl group, C₃₋₁₀ cycloalkyl group or C₅₋₆ cycloalkenyl group, especially preferably, C₁₋₃ alkyl group or a substituted C₁₋₃ alkyl group. The C₁₋₆ alkyl group is, also here, preferably one of those described in the foregoing and may be exemplified by methyl, ethyl, n-propyl, isopropyl, n-butyl, isobutyl, sec-butyl, tert-butyl, n-pentyl or n-hexyl, especially preferably, methyl, ethyl and n-propyl. The C₂₋₆ alkenyl group is, also here, preferably one of those described in the foregoing and may be exemplified by vinyl, allyl, isopropenyl, methallyl, 1,1-dimethylallyl, 2-butenyl or 3-butenyl. The C₂₋₆ alkynyl group may be exemplified by ethynyl, 1-propynyl, 2-propynyl or propargyl. The C₃₋₁₀ cycloalkyl group is, also here, preferably the above-mentioned C₃₋₈ cycloalkyl group and may be exemplified by cyclopropyl, cyclobutyl, cyclopentyl, cyclohexyl, cycloheptyl or adamantyl. The C₅₋₆ cycloalkenyl group may be exemplified by 2-cyclopentenyl, 3-cyclopentenyl, 2-cyclohexenyl, 3-cyclohexenyl, cyclopentadienyl or cyclohexadienyl. Substituents of these hydrocarbon residues may be one to three groups exemplified by hydroxyl group, C₁₋₆ alkyl group, C₂₋₆ akenyl group, C₂₋₆ alkynyl group, C₃₋₁₀ cycloalkyl group, C₅₋₆cycloalkenyl group, C₆₋₁₀ aryl group, C₇₋₁₉ aralkyl group, heterocyclic group, C₁₋₆ alkoxy group, C₃₋₁₀ cycloalkoxyloxy group, C₆₋₁₀ aryloxy group, C₇₋₁₉ aralkyloxy group, heterocycle-oxy group, mercapto group, C₁₋₆ alkylthio group, C₃₋₁₀ cycloalkylthio group, C₆₋₁₀ arylthio group, C₇₋₁₉ aralkylthio group, heterocycle-thio group, amino group, mono-C₁₋₆ alkylamino group, di-C₁₋₆ alkylamino group, tri-C₁₋₆ alkylammonium group, C₃₋₁₀ cycloalkylamino group, C₆₋₁₀ arylamino group, C₇₋₁₉ aralkylamino group, heterocycle-amino group, cyclic amino group, azido group, nitro group, halogen atom, cyano group, carboxyl group, C₁₋₁₀ alkoxycarbonyl group, C₆₋₁₀ aryloxy-carbonyl group, C₇₋₁₉ aralkyloxy-carbonyl group, C₆₋₁₀ aryl-acyl⁺ group, C₁₋₆ alkanoyl group, C₃₋₅ alkenoyl group, C₆₋₁₀ arylacyl⁺oxy group, C₂₋₆ alkanoyloxy group, C₃₋₅ alkenoyloxy group, carbamoyl* group, thiocarbamoyl* group, carbamoyl*oxy group, phthalimido group, C₁₋₆ alkanoylamino group, C₆₋₁₀ aryl-acyl⁺amino group, carboxyamino group, C₁₋₁₀ alkoxy-carboxamido group, C₆₋₁₀ aryloxy-carboxamido group or C₇₋₁₉ aralkyloxy-carboxamido group, and two or three of them, same or different, may be present. As substituents of the hydrocarbon residues, more specifically stating, the C₁₋₆ alkyl group stands for the above-mentioned groups, i.e. methyl, ethyl, n-propyl, isopropyl, n-butyl, isobutyl, sec-butyl, tert-butyl, n-pentyl or n-hexyl, the C₂₋₆ alkenyl group stands for the above-mentioned groups, i.e. vinyl, allyl, isopropenyl, methallyl, 1,1-dimethylallyl, 2-butenyl or 3-butenyl, the C₂₋₆ alkynyl group stands for the above-mentioned groups, i.e. ethynyl, 1-propynyl, 2-propynyl or propargyl, the C₃₋₁₀ cycloalkyl group stands for the above-mentioned groups, i.e. cyclopropyl, cyclobutyl, cyclopentyl, cyclohexyl, cycloheptyl or adamantyl, the C₅₋₆ cycloalkenyl group stands for the above-mentioned groups, i.e. cyclopropenyl, 2-cyclopentenyl, 3-cyclopentenyl, 2-cyclohexenyl, 3-cyclohexenyl, cyclopentadienyl or cyclohexadienyl, the C₆₋₁₀ aryl group stands for the above-mentioned groups, i.e. phenyl, naphthyl or biphenylyl, the C₇₋₁₉ aralkyl group stands for the above-mentioned groups, i.e. benzyl, 1-phenylethyl, 2-phenylethyl, phenylpropyl, naphthylmethyl, or benzhydryl, the C₁₋₆ alkoxy group stands for the above-mentioned groups, i.e. methoxy, ethoxy, n-propoxy, isopropoxy, n-butoxy, tert-butoxy, n-pentyloxy or n-hexyloxy, the C₃₋₁₀ cycloalkyloxy group stands for the above-mentioned groups, i.e. cyclopropyloxy or cyclohexyloxy, the C₆₋₁₀ aryloxy group stands for the above-mentioned groups, i.e. phenoxy or naphthyloxy, the C₇₋₁₉ aralkyloxy group stands for the above-mentioned groups, i.e. benzyloxy, 1-phenylethyloxy, 2-phenylethyloxy or benzhydryloxy, the C₁₋₆ alkylthio group stands for the above-mentioned groups, i.e. methylthio, ethylthio, n-propylthio or n-butylthio, the C₃₋₁₀ cycloalkylthio group stands for the above-mentioned groups, i.e. cyclopropylthio or cyclohexylthio, the C₆₋₁₀ arylthio group stands for the above-mentioned groups, i.e. phenylthio or naphthylthio, the C₇₋₁₉ aralkylthio group stands for the above-mentioned groups, i.e. benzylthio, phenylethylthio or benzhydrylthio, the mono-C₁₋₆ alkylamino group stands for the above-mentioned groups, i.e. methylamino, ethylamino, n-propylamino, or n-butylamino, the di-C₁₋₆ alkylamino group stands for the above-mentioned groups, i.e. dimethylamino, diethylamino, methylethylamino, di-(n-propyl)amino or di-(n-butyl)amino, the tri-C₁₋₆ alkylammonium group stands for the above-mentioned groups, i.e. trimethylammonium or triethylammonium, the C₃₋₁₀ cycloalkylamino group stands for the above-mentioned groups, i.e. cyclopropylamino, cyclopentylamino or cyclohexylamino, the C₆₋₁₀ arylamino group stands for the above-mentioned groups, i.e. anilino or N-methylanilino, the C₇₋₁₉ aralkylamino group stands for the above-mentioned groups, i.e. benzylamino, 1-phenylethylamino, 2-phenylethylamino or benzhydrylamino, the cyclic amino group stands for the above-mentioned groups, i.e. pyrrolidino, piperidino, piperazino, morpholino or 1-pyrrolyl, the halogen atom stands here for fluorine, chlorine, bromine or iodine, the C₁₋₁₀ alkoxy-carbonyl group stands for the above-mentioned groups, i.e. methoxycarbonyl, ethoxycarbonyl, n-propoxycarbonyl, isopropoxycarbonyl, n-butoxycarbonyl, isobutoxycarbonyl, tert-butoxycarbonyl, cyclopentyloxycarbonyl, cyclohexyloxycarbonyl or norbornyloxycarbonyl, the C₆₋₁₀ aryloxycarbonyl group stands for the above-mentioned groups, i.e. phenoxycarbonyl or naphthyloxycarbonyl, the C₇₋₁₉ aralkyloxycarbonyl group stands for the above-mentioned groups, i.e. benzyloxycarbonyl or benzhydryloxycarbonyl, the C₆₋₁₀ arylacyl⁺ group stands for the above-mentioned groups, i.e. benzoyl, naphthoyl, phthaloyl or phenylacetyl, the C₁₋₆ alkanoyl group stands for the above-mentioned groups, i.e. formyl, acetyl, propionyl, butyryl, valeryl, pivaloyl, succinyl or glutaryl, the C₃₋₅ alkenoyl group stands for the above-mentioned groups, i.e. acryloyl, crotonoyl or maleoyl, the C₆₋₁₀ aryl-acyl⁺oxy group stand for the above-mentioned groups, i.e. benzoyloxy, naphthoyloxy or phenylacetoxy, the C₂₋₆ alkanoyloxy group stands for the above-mentioned groups, i.e. acetoxy, propionyloxy, butyryloxy, valeryloxy or pivaloyloxy, the C₃₋₅ alkenoyloxy group stands for the above-mentioned groups, i.e. acryloyloxy or crotonoyloxy, the carbamoyl* group stands for the above-mentioned groups, i.e. carbamoyl, N-methylcarbamoyl, N-ethylcarbamoyl, N,N-dimethylcarbamoyl, N-ethylcarbamoyl, N,N-diethylcarbamoyl, N-phenylcarbamoyl, N-acetylcarbamoyl, N-benzoylcarbamoyl, N-(p-methoxyphenyl)carbamoyl and, in addition, pyrrolidinocarbonyl, piperidinocarbonyl, piperazinocarbonyl or morpholinocarbonyl, the thiocarbamoyl* group stands for the above-mentioned groups, i.e. thiocarbamoyl, N-methylthiocarbamoyl or N-phenylthiocarbonyl, the carbamoyl*oxy group stands for the above-mentioned group, i.e. carbamoyloxy, N-methylcarbamoyloxy, N,N-dimethylcarbamoyloxy, N-ethylcarbamoyloxy or N-phenylcarbamoyloxy, "C₁₋₆ alkanoylamino group" stands for e.g. acetamido, propionamido, butyramido, valeramido or pivalamido, "C₆₋₁₀ aryl-acyl⁺amino group stands for e.g. benzamido, naphthoylamido or phthalimido, "C₁₋₁₀ alkoxy-carboxamido group" stands for e.g. methoxycarboxamido (CH₃OCONH-), ethoxycarboxamido or tert-butoxycarboxamido, "C₆₋₁₀ aryloxy-carboxamido group" stands for e.g. phenoxycarboxamido (C₆H₅OCONH-), and "C₇₋₁₉ aralkyloxycarboxamido group" stands for e.g. benzyloxycarboxamido (C₆H₅CH₂OCONH-) or benzhydryloxycarboxamido. The heterocyclic group, heterocyclic groups of heterocycle-oxy group, heterocycle-thio group and heterocycle-amino group are also here such groups as formed by removing one hydrogen atom bonding to the carbon atom of the heterocyclic ring. Such a heterocyclic ring as above may be exemplified by a 5- to 8-membered ring containing one to several, preferably 1 to 4, hetero atoms such as an oxygen atom or sulfur atom. Such heterocyclic groups may be exemplified also here by those concretely mentioned above, including 2-pyrrolyl. Hence, "heterocycle-oxy group" is exemplified by thiazolyloxy, and "heterocycle-thio group" is exemplified by thiazolylthio, and "heterocycle-amino group" is exemplified by thiazolylamino or thiadiazolylamino. Preferable substituted hydrocarbon residues are C₁₋₃ alkyl groups (C₁₋₃ alkyl group means methyl, ethyl, n-propyl, isopropyl, etc.) substituted by 1 to 3 groups such as hydroxyl group, cycloalkyl group, alkoxy group, alkylthio group, amino group, trialkylammonium group, halogen atom, carboxyl group, alkoxycarbonyl group, carbamoyl group, cyano group, azido group or heterocyclic group, which may concretely be mentioned, among many others, cyclopropylmethyl, methoxymethyl, ethoxymethyl, 1-methoxyethyl, 2-methoxyethyl, 1-ethoxyethyl, 2-hydroxyethyl, methylthiomethyl, 2-aminoethyl, 2-(trimethylammonium)ethyl, 2-(triethylammonium)ethyl, fluoromethyl, difluoromethyl, trifluoromethyl, 2-fluoroethyl, 2,2,-difluoroethyl, chloromethyl, 2-chloroethyl, 2,2-dichloroethyl, 2,2,2-trichloroethyl, 2-bromoethyl, 2-iodoethyl, 2,2,2-trifluoroethyl, carboxymethyl, 1-carboxyethyl, 2-carboxyethyl, 2-carboxypropyl, 3-carboxypropyl, 1-carboxybutyl, cyanomethyl, 1-carboxy-1-methylethyl, methoxycarbonylmethyl, ethoxycarbonylmethyl, tert-butoxycarbonylmethyl, 1-methoxycarbonyl-1-methylethyl, 1-ethoxycarbonyl-1-methylethyl, 1-tert-butoxycarbonyl-1-methylethyl, 1- benzyloxycarbonyl-1-methylethyl, 1-pivaloyloxycarbonyl-1-methylethyl, carbamoylmethyl, 2-azidoethyl, 2-(pyrazolyl)ethyl, 2-(imidazolyl)ethyl, 2-(2-oxopyrrolidin-3-yl)ethyl or 2-amino-4-thiazolylmethyl. Most preferable ones among the above-exemplified hydrocarbon residues are straight-chain C₁₋₃ alkyl groups, e.g. methyl, ethyl and n-propyl; straight-chain or branched C₁₋₃ alkyl groups substituted by 1 to 3 groups such as halogen atom, hydroxyl group, alkoxy group, carboxyl group, alkoxycarbonyl group or cyano group, e.g. 2-fluoroethyl, 2-chloroethyl, 2-hydroxyethyl, 2-methoxyethyl, cyanomethyl, carboxymethyl, tert-butoxycarbonylmethyl, 1-carboxy-1-methylethyl or 1-tert-butoxycarbonyl-1-methylethyl; allyl group and propargyl group. Supposing here that the symbol R 3' should stand for most preferable hydrocarbon residues exemplified above or a hydrogen atom, the compound [I] of this invention is shown by the following structural formula: (wherein symbols are of the same meaning as defined above). Preferable examples of the acyl group shown by the formula: are 2-(5-amino-1,2,4-thiadiazol-3-yl)-2(Z)-(hydroxyimino)acetyl, 2-(5-amino-1,2,4-thiadiazol-3-yl)-2(Z)-(methoxyimino)acetyl, 2-(5-amino-1,2,4-thiadiazol-3-yl)-2(Z)-(ethoxyimino)-acetyl, 2-(5-amino-1,2,4-thiadiazol-3-yl)-2(Z)-(ethoxyimino)acetyl, 2-(5-amino-1,2,4-thiadiazol-3-yl)-2(Z)-[(2-fluoroethyl)oxyimino]acetyl, 2-(5-amino-1,2,4-thiadiazol-3-yl)-2(Z)-[(2-chloroethyl)oxyimino]acetyl, 2-(5-amino-1,2,4-thiadiazol-3-yl)-2(Z)-(carboxymethyloxyimino)acetyl, 2-(5-amino-1,2,4-thiadiazol-3-yl)-2(Z)-[(1-carboxy-1-methylethyl)oxyimino]acetyl, 2-(5-amino-1,2,4-thiadiazol-3-yl)-2(Z)-[(1-tert-butoxycarbonyl-1-methylethyl)oxyimino]acetyl. The substituent R⁴ in the compound [I] of this invention stands for hydrogen atom, methoxy group or formamido group (HCONH-). The substituent R¹³ in the compound (I) of this invention stands for hydrogen atom, methyl group, hydroxyl group or halogen atom. The halogen atom means here fluorine, chlorine, bromine or iodine. In the compound (I) of this invention, the substituent A ⊕ stands for imidazolium-1-yl group which forms a condensed ring at 2,3- or 3,4-position. Condensed ring means an imidazole ring having a 5- to 6-membered aromatic heterocyclic ring condensed therewith, and it may optionally be further condensed with another aromatic ring or aromatic heterocyclic ring. The mark ⊕ attached to the right shoulder of the substituent A means that A has a monovalent positive electric charge. The optionally substituted imidazolium-1-yl group (A ⊕ ) forming the condensed ring at the 2,3- or 3,4- position is shown by the general formula [A¹] or [A²]; wherein B stands for a group forming a 5- to 6-membered aromatic heterocyclic ring which may be condensed with another aromatic ring or aromatic heterocyclic ring, R¹¹ stands for hydrogen atom or a substituent (or substituents) on the imidazole ring, and R¹² stands for hydrogen atom or a substituent (or substituents) on the ring which is condensed with the imidazole ring. B consists of carbon atom, nitrogen atom, oxygen atom and/or sulfur atom, and, among them, a carbon atom combines with one hydrogen atom or one substituent, or forms another condensed ring together with an adjacent carbon atom. The A¹ group may be embodied as follows, for example The A² group may be embodied as follows, for example; Among these groups, especially preferable are imidazo(1,2-a)pyridinium-1-yl imidazo(1,2-b)pyridazinium-1-yl and imidazo(1,5-a)pyridinium-2-yl In the above-mentioned formulae [A¹] and [A²] as well as in A¹ groups and A² groups embodied as above, the positive electric charge A ⊕ is applied, for convenience sake, to the nitrogen atom at the 3-position of imidazole, but there may be a case where the said quaternary nitrogen is that of the nitrogen atom at the 1-position. Further, there may be cases where the monovalent positive electric charge is delocalized at the imidazole ring, or even delocalized on the entire condensed ring. Therefore, the above may include or The position which this positive electric charge takes varies with, among others, the state (solid or in solution) of the compound (I), kinds of solvents, pH, temperature or kinds of substituents. Accordingly, the present invention includes all the cases where the positive electric charge is localized at a nitrogen atom or is delocalized on the entire condensed ring. The number of the substituents R¹¹ and R¹² is preferably one to two. The substituents R¹¹ and R¹² on the condensed ring A may be exemplified by a hydroxyl group, hydroxy C₁₋₆ alkyl group, C₁₋₆ alkyl group, C₂₋₆ alkenyl group, C₂₋₆ alkynyl group, C₄₋₆ alkadienyl group, C₃₋₁₀ cycloalkyl group, C₅₋₆ cyclo alkenyl group, C₃₋₁₀ cycloalkyl C₁₋₆ alkyl group, C₆₋₁₀ aryl group, C₇₋₁₂ aralkyl group, di-C₆₋₁₀ aryl methyl group, tri-C₆₋₁₀ arylmethyl group, heterocyclic group, C₁₋₆ alkoxy group, C₁₋₆ alkoxy C₁₋₆ alkyl group, C₃₋₁₀ cycloalkyloxy group, C₆₋₁₀ aryloxy group, C₇₋₁₉ aralkyloxy group, mercapto group, mercapto C₁₋₆ alkyl group, sulfo group, sulfo C₁₋₆ alkyl group, C₁₋₆ alkylthio group, C₁₋₆ alkylthio C₁₋₆ alkyl group, C₃₋₁₀ cycloalkylthio group, C₆₋₁₀ arylthio group, C₇₋₁₉ aralkylthio group, amino group, amino C₁₋₆ alkyl group, mono C₁₋₆ alkylamino group, di-C₁₋₆ alkylamino group, mono-C₁₋₆ alkylamino C₁₋₆ alkyl group, di-C₁₋₆ alkylamino C₁₋₆ alkyl group, C₃₋₁₀ cycloalkylamino group, C₆₋₁₀ arylamino group, C₇₋₁₉ aralkylamino group, cyclic amino group, cyclic amino C₁₋₆ alkyl group, cyclic amino C₁₋₆ alkylamino group, azido group, nitro group, halogen atom, halogeno C₁₋₆ alkyl group, cyano group, cyano C₁₋₆ alkyl group, carboxyl group, carboxy C₁₋₆ alkyl group, C₁₋₁₀ alkoxy-carbonyl group, C₁₋₁₀ alkoxy-carbonyl C₁₋₆ alkyl group, C₆₋₁₀ aryloxy carbonyl group, C₇₋₁₉ aralkyloxy-carbonyl group, C₆₋₁₀ aryl-acyl⁺-group, C₁₋₆ alkanoyl group, C₂₋₆ alkanoyl C₁₋₆ alkyl group, C₃₋₅ alkenoyl group, C₆₋₁₀ aryl-acyl⁺oxy group, C₂₋₆ alkanoyloxy group, C₂₋₆ alkanoyloxy C₁₋₆ alkyl group, C₃₋₅ alkenoyloxy group, carbamoyl C₁₋₆ alkyl group, carbamoyl* group, thiocarbamoyl* group, carbamoyl*oxy group, carbamoyloxy C₁₋₆ - alkyl group, C₁₋₆ alkanoylamino group, C₆₋₁₀ aryl-acyl⁺amino group, sulfonamido group, carboxyamino group, C₁₋₁₀ alkoxy-carboxamido group, C₆₋₁₀ aryloxy-carboxamido group or C₇₋₁₉ aralkyloxy-carboxamido group. Among the above-mentioned substituents, "C₄₋₆ alkadienyl group" is exemplified by 1,3-butadienyl, "C₃₋₁₀ cycloalkyl C₁₋₆ alkyl group" is exemplified by cyclopentylmethyl or cyclohexylmethyl, and halogen atom means here fluorine, chlorine or bromine. All the groups other than the above may be exemplified as in the foregoing. These substituents may occur singly or in plurality being the same or different ones. And, in A¹, the 5,6-position of the imidazole ring may be condensed with an alicyclic ring, aromatic ring or heterocyclic ring. As the examples, the following may be counted: In the above, B and R¹² are of the same significance as afore-defined. The above-mentioned R¹¹ and R¹² may be further substituted. In the above compound (I), the mark ⊖ attached to the right shoulder of the carboxyl substituent (-COO) means that the said carboxyl group is a carboxylate anion and forms internal salt by making a pair with the positive electric charge on the substituent A. On the other hand, the compound (I) may be its pharmaceutically acceptable salt or ester. As the pharmaceutically acceptable salt, there may be mentioned, among others, inorganic base salts, ammonium salt, organic base salts, inorganic acid addition salts, organic acid addition salts and basic amino acid salts. There may be exemplified an alkali metal (e.g. sodium, potassium etc.) or an alkaline earth metal (e.g. calcium) as an inorganic base capable of giving the inorganic base salts; procaine, 2-phenylethylbenzylamine, dibenzylethylenediamine, ethanolamine, diethanolamine, tris-hydroxymethylaminomethane, poly-hydroxyalkylamine or N-methylglucosamine as an organic base capable of giving organic base salts, hydrochloric acid, hydrobromic acid, sulfuric acid, nitric acid or phosphoric acid as an inorganic acid capable of giving the inorganic acid addition salts; p-toluenesulfonic acid, methanesulfonic acid, formic acid, trifluoroacetic acid or maleic acid as an organic acid capable of giving organic acid addition salts; and lysine, arginine, ornithine or histidine as a basic amino acid capable of giving basic amino acid salts. Among these salts, basic salts (i.e. inorganic base salts, ammonium salt, organic base salts and basic amino acid salts) mean salts derivable in case there is (are) acidic group(s) e.g. carboxyl group, sulfo group etc. on the substituent R¹, R³ or A of the compound (I), and acid addition salts (i.e. inorganic acid addition salts and organic acid addition salts) mean salts derivable in case there is (are) basic group(s) e.g. amino group, mono alkylamino group, dialkylamino group, cycloalkylamino group, arylamino group, aralkylamino group, cyclic amino group, nitrogen-containing heterocyclic group etc. on the substituent R¹, R³ or A of the compound (I). Incidentally, the acid addition salt also includes an intramolecular salt of the compound (I) i.e. a salt having carboxyl(COOH) group at the 4-position and CH₂A ⊕ .M ⊖ group (wherein M ⊖ denotes an anion formed by removal of a proton (H ⊕ ) from inorganic acid or organic acid; such an anion is exemplified by chloride ion, bromide ion, sulfate ion, p-toluenesulfonate ion, methanesulfonate ion, trifluoroacetat ion) at the 3-position, which is formed through addition of one mole of acid to carboxylate(COO ⊖ ) group of the 4-position and CH₂A ⊕ group of the 3-position of the compound (I). The ester derivatives of the compound (I) mean esters derivable by esterifying the carboxyl group contained in the molecule, which include esters usable as synthetic intermediates and bioavailably unstable non-toxic esters. The esters usable as synthetic intermediates are exemplified by a C₁₋₆ alkyl* ester, C₂₋₆ alkenyl ester, C₃₋₁₀ cycloalkyl ester, C₃₋₁₀ cycloalkyl C₁₋₆ alkyl ester, C₆₋₁₀ aryl* ester, C₇₋₁₂ aralkyl*ester, di-C₆₋₁₀ arylmethyl ester, tri-C₆₋₁₀ arylmethyl ester or substituted silyl ester. There may be exemplified, as "C₁₋₆ alkyl* group" capable of giving C₁₋₆ alkyl* ester, methyl, ethyl, n-propyl, isopropyl, n-butyl, isobutyl, sec-butyl, tert-butyl, n-pentyl, n-hexyl, benzyloxymethyl, 2-methylsulfonylethyl, 2-trimethylsilylethyl, 2,2,2-trichloroethyl, 2-iodoethyl, acetylmethyl, p-nitrobenzoylmethyl, p-mesylbenzoylmethyl, phthalimidomethyl, succinimidomethyl, benzenesulfonylmethyl, phenylthiomethyl, dimethylaminoethyl, pyridine-1-oxido-2-methyl, methylsulfinylmethyl, or 2-cyano-1,1-dimethylethyl; as C₂₋₆ alkenyl group capable of giving C₂₋₆ alkenyl ester, the afore-mentioned ones, i.e. vinyl, allyl, 1-propenyl, isopropenyl, 1-butenyl, 2-butenyl, 3-butenyl, methallyl, 1,1-dimethylallyl or 3-methyl-3-butenyl; as C₃₋₁₀ cycloalkyl group capable of giving C₃₋₁₀ cycloalkyl ester, the aforementioned ones, i.e. cyclopropyl, cyclobutyl, cyclopentyl, cyclohexyl, cycloheptyl, norbornyl or adamantyl; as C₃₋₁₀ cycloalkyl C₁₋₆ alkyl group capable of giving C₃₋₁₀ cycloalkyl C₁₋₆ alkyl ester, the afore-mentioned ones, i.e. cyclopropylmethyl, cyclopentylmethyl or cyclohexylmethyl; as "C₆₋₁₀ aryl*group" capable of giving C₆₋₁₀ aryl*ester, phenyl, alpha-naphthyl, β-naphthyl, biphenylyl, p-nitrophenyl or p-chlorophenyl; as "C₇₋₁₂ aralkyl* group" capable of giving C₇₋₁₂ aralkyl*ester, benzyl, 1-phenylethyl, 2-phenylethyl, phenylpropyl, naphthylmethyl, p-nitrobenzyl, p-methoxybenzyl, 1-indanyl, phenacyl or 3,5-di-tert-butyl-4-hydroxybenzyl; as di-C₆₋₁₀ aryl-methyl group capable of giving di C₆₋₁₀ aryl-methyl ester, the afore-mentioned ones, i.e. benzhydryl or bis(p-methoxyphenyl)methyl; as tri-C₆₋₁₀ aryl-methyl group capable of giving tri-C₆₋₁₀ aryl-methyl ester, the afore-mentioned ones, i.e. trityl; and as substituted silyl group capable of giving substituted silyl ester, the afore-mentioned ones, i.e. trimethylsilyl, tert-butyldimethylsilyl or -Si(CH₃)₂CH₂CH₂Si(CH₃)₂-. The above esters include esters at the 4-position. Such compound having above ester group at the 4-position forms an intramolecular salt of CH₂A ⊕ .M ⊖ (wherein M ⊖ has the same meaning as defined above) at the 3-position. As the biovailably unstable and non-toxic esters, those which have been confirmed as employable in the fields of penicillin and cephalosporin can conveniently be employed also in the present invention, which may be exemplified by C₂₋₆ alkanoyloxy C₁₋₆ alkyl ester, 1-(C₁₋₆ alkoxy)C₁₋₆ alkyl ester, 1-(C₁₋₆ alkylthio)C₁₋₆ alkylthio ester or 1-(C₁₋₆ alkoxycarbonyloxy)C₁₋₆ alkyl ester. The C₂₋₆ alkanoyloxy C₁₋₆ alkyl ester is exemplified by acetoxymethyl ester, 1-acetoxyethyl ester, 1-acetoxybutyl ester, 2-acetoxyethyl ester, propionyloxymethyl ester, pivaloyloxymethyl ester. The 1-(C₁₋₆ alkoxy)C₁₋₆ alkyl ester is exemplified by methoxymethyl ester, ethoxymethyl ester, isopropoxymethyl ester, 1-methoxyethyl ester of 1-ethoxyethyl ester. The 1-(C₁₋₆ alkylthio)C₁₋₆ alkyl ester is exemplified by methylthiomethyl ester or ethylthiomethyl ester. The 1-(C₁₋₆ alkoxycarbonyloxy)C₁₋₆ alkyl ester is exemplified by 1-(ethoxycarbonyloxy)ethyl ester or 1-(ter-butoxycarbonyloxy)ethyl ester. The present invention includes besides the above-mentioned ester derivatives pharmaceutically acceptable compounds which are convertible in vivo to the compound (I). The above-mentioned esters usable as synthetic intermediates and bioavailably unstable non-toxic esters include esters at the 4-position. Such esters at the 4-position usually form an intramolecular salt of CH₂A ⊕ . M ⊖ (wherein M ⊖ has the same meaning as defined above) at the 3-position. When the compund (I) has a hydroxyl group, the hydroxyl group may be protected. Groups usable for protecting the hydroxyl group include those which are usually employed for protecting the hydroxyl group in the filed of β-lactam and organic chemistry, which may be exemplified by, besides the afore-mentioned C₂₋₆ alkanoyl groups, substituted oxycarbonyl group, tert-butyl group, C₇₋₁₂ aralkyl*group, di-C₆₋₁₀ aryl-methyl group, a tri-C₆₋₁₀ aryl-methyl group, 1-(C₁₋₆ alkoxy)C₁₋₆ alkyl group, 1-(C₁₋₆ alkylthio)C₁₋₆ alkyl group and substituted silyl group, acetal residues e.g. 2-tetrahydropyranyl or 4-methoxy-4-tetrahydropyranyl. When the compound (I) additionally has an amino group other than those mentioned above, the amino group may also be protected. Groups employable for protecting those amino groups are exemplified also here by those referred to in the protection of the afore-mentioned amino groups. The compound (I) of this invention has a broad antibacterial spectrum and can be used for prophylaxis and therapy of various diseases of men and animals caused by pathogenic bacteria, for example, infections of respiratory tract or of urinary passages. Characteristic features of the antibacterial spectrum of the antibacterial compound (I) are menioned as follows: (1) remarkably strong activity against a variety of gram-negative bacteria; (2) strong activity against gram-positive bacteria (e.g. Staphylococcus aureaus or Cornyebacterium diphteriae) ; (3) remarkably effective against Pseudomonas aeruginosa which are not sensitive to therapy with conventional cephalosporin-type antibiotics; and (4) Strong activity against a variety of β-lactamase-producing gram-negative bacteria (e.g. the genera Escherichia , Enterobacter , Serratia or Proteus ).Especially against bacteria belonging to the genus Pseudomonas , to which aminoglycoside antibiotics such as Amikacin or Gentamicin have been used, the antibacterial compound (I) shows antibacterial activity comparable to these aminoglycosides with remarkably lower toxicity to men and animals, which is counted as one of the great advantages. Besides, the antibacterial compound (I) of the present invention has the following characteristic features: i.e. excellent stability, high concentration in blood, long duration of effect and remarkably high concentration in tissue. Among the compounds (I) of this invention, the compound having a following structure is preferable: (1) A ⊕ is unsubstituted imidazo[1,2-b]pyridazinium-1-yl group; (2) A ⊕ is imidazo[1,5-a]pyridinium-2-yl group which is substituted by a C₁₋₆ alkyl group, halogen atom, or cyano group; or (3) R¹ is an amino group, R³ is an optionally substituted C₁₋₃ alkyl group; and A ⊕ is an imidazo[1,2-a]pyridinium-1-yl group which is substituted by a fluorine or cyano group. How to make the compound (I) of this invention, its salt or ester will be described in detail as follows. The processes described hereafter are all conventional as reactions per se, and analogous ones thereto can also be applied. The compound (I) of the present invention can be produced by conventional methods, which are mentioned below. Production method (1) The compound (I) can be synthesized by reacting the 7-amino compound of the formula wherein the symbols Z, R⁴, R¹³ and A ⊕ are of the same meaning as defined above or a salt or ester thereof with carboxylic acid of the formula (this compound may be referred to as "R b OH" hereinafter) wherein the symbols R¹ and R³ are of the same meaning as defined above, or a salt or reactive derivative thereof. This is a method of subjecting a 7-amino compound (II) or a salt or ester thereof (the 7-amino compound (II), and salt and ester thereof may simply be abbreviated hereinafter as the 7-amino compound (II)) to acylation with carboxylic acid R b OH or a salt or reactive derivative thereof. In this method, the carboxylic acid R b OH in the free form, a salt or reactive derivative thereof is used as the acylating agent of the 7-amino group of the 7-amino compound (II). More concretely, the free acid R b OH or a salt or reactive derivative of the free acid R b OH, such as an inorganic base salt, organic base salt, acid halide, acid azide, acid anhydride, mixed acid anhydride, active amide, active ester or active thioester is used for the acylation. There may be mentioned, among others, as inorganic base salts, alkali metal salts (e.g. sodium salt, potassium salt, etc.), or alkaline earth metal salts (e.g. calcium salt, etc.); as organic base salts, trimethylamine salt, triethylamine salt, tert-butydimethylamine salt, dibenzylmethylamine salt, benzyldimethylamine salt, N,N-dimethylaniline salt, pyridine salt or quinoline salt; as acid halide, acid chloride or acid bromide; as mixed acid anhydride, mono C₁₋₆ alkyl carbonic acid mixed anhydride (e.g. mixed acid anhydride of the free acid R b OH with, for example, monomethyl carbonic acid, monoethyl carbonic acid, monoisopropyl carbonic acid, monoisobutyl carbonic acid, mono-tert-butyl carbonic acid, monobenzyl carbonic acid, mono(p-nitrobenzyl)carbonic acid, or monoallyl carbonic acid), C₁₋₆ aliphatic carboxylic acid mixed anhydride (e.g. mixed acid anhydride of the free acid R b OH with, for example, acetic acid, trichloroacetic acid, cyanoacetic acid, propionic acid, butyric acid, isobutyric acid, valeric acid, isovaleric acid, pivalic acid, trifluoroacetic acid, trichloroacetic acid or acetoacetic acid), C₇₋₁₂ aromatic carboxylic acid mixed anhydride (e.g. mixed acid anhydride of the free acid R b OH with, for example, benzoic acid, p-toluic acid or p-chlorobenzoic acid), organic sulfonic acid mixed anhydride (e.g. mixed acid anhydride of the free acid R b OH with, for example, methanesulfonic acid, ethanesulfonic acid, benzenesulfonic acid or p-toluenesulfonic acid); as active amide, an amide with a nitrogen-containing heterocyclic compound (e.g. acid amide of the free acid R b OH with, for example, pyrazole, imidazole or benzotriazole, these nitrogen-containing heterocyclic compounds being optionally substituted with afore-mentioned C₁₋₆ alkyl group, C₁₋₆ alkoxy group, halogen atom, oxo group, thioxo group or C₁₋₆ alkylthio group). As the active ester, those which can be used for the same purpose in the fields of β-lactam and peptide synthesis can all be used, which are exemplified by - besides organic phosphoric acid ester (e.g. diethoxy phosphoric acid ester or diphenoxy phosphoric acid) -, p-nitrophenyl ester, 2,4-dinitrophenyl ester, cyanomethyl ester, pentachlorophenyl ester, N-hydroxysuccinimide ester, N-hydroxyphthalimide ester, 1-hydroxybenzotriazole ester, 6-chloro-1-hydroxybenzotriazole ester, 1-hydroxy-1H-2-pyridone ester. The active thioester can be exemplified by esters with aromatic heterocyclic thiol compounds (e.g. 2-pyridylthiol ester, 2-benzothiazolylthiol ester, these heterocyclic rings being substituted with afore-mentioend C₁₋₆ alkyl group, C₁₋₆ alkoxy group, halogen atom or C₁₋₆ alkylthio group). On the other hand, the 7-amino compound (II) can be used as free base, a salt or ester thereof. Salts of the 7-amino compound (II) are exemplified by inorganic base salts, ammonium salt, organic base salts, inorganic acid addition salts or organic acid addition salts. There may be mentioned, as inorganic base salts, alkali metal salts (e.g. sodium salts or potassium salts) and alkaline earth metal salts (e.g. calcium salts); as organic base salts, for example trimethylamine salts, triethylamine salts, tert-butyldimethylamine salts, dibenzylmethylamine salts, benzyldimethylamine salts, N,N-dimethylaniline salts, pyridine salts or quinoline salts; as inorganic acid addition salts, for example hydrochlorides, hydrobromides, sulfates, nitrates or phosphates; and as organic acid addition salts, formates, acetates, trifluoroacetates, methanesulfonates, or p-toluenesulfonates. As the esters of the 7-amino compound (II), esters already referred to as ester derivatives of the compound (I) can also be counted, more concretely, C₁₋₆ alkyl* ester, C₂₋₆ alkenyl ester, C₃₋₁₀ cycloalkyl ester, C₃₋₆ cycloalkyl C₁₋₆ alkyl ester, C₆₋₁₀ aryl*ester, C₇₋₁₂ aralkyl*ester, di-C₆₋₁₀ aryl-methyl ester, tri-C₆₋₁₀ aryl-methyl ester or C₂₋₆ alkanoyloxy C₁₋₆ alkyl ester. The starting material R b OH as well as salts and reactive derivatives thereof can be easily prepared by known methods or analogous methods thereto. A reactive derivative of the compound R b OH, after isolation from the reaction mixture, can be allowed to react with a 7-amino compound (II), or as the reaction mixture containing the reactive derivative of the compound R b OH before the isolation, it can be allowed to react with a 7-amino compound (II). When the carboxylic acid R b OH is used in the state of its free acid or salt, a suitable condensing agent is employed. As the condensing agents, there may be counted N,N'-di-substituted carbodiimides e.g. N,N'-di-cyclohexylcarbodiimide; azolides e.g. N.N'-carbonyldiimidazole or N,N'-thiocarbonyldiimidazole; dehydrating agents e.g. N-ethoxycarbonyl-2-ethoxy-1,2-dihydroquinoline, phosphorus oxychloride or alkoxy acetylene; 2-halogenopyridinium salts, e.g. 2-chloropyridinium methyl iodide or 2-fluoropyridinium methyl iodide. The reactions where these condensing agents are employed are considered to proceed via reactive derivatives of the carboxylic acid R b OH. These reactions are generally conducted in a solvent which does not hamper the reaction. These solvents may be exemplified by ethers such as dioxane, tetrahydrofuran, diethyl ether, tert-butyl methyl ether, di-isopropyl ether or ethylene glycol dimethyl ether; esters such as ethyl formate, ethyl acetate or n-butyl acetate; halogenated hydrocarbons such as dichloromethane, chloroform, carbon tetrachloride, trichlene or 1,2-dichloroethane; hydrocarbons such as n-hexane, benzene or toluene; amides such as formamide, N,N-dimethylformamide or N,N-dimethylacetamide; ketones such as acetone, methyl ethyl ketone or methyl isobutyl ketone; or nitriles such as acetonitrile or propionitrile and, besides, dimethyl sulfoxide, sulfolane, hexamethylphosphoramide or water, singly or in combination. The amount of acylating agent (R b OH) or a salt or reactive derivative thereof is usually about 1 to 5 mol, preferably about 1 to 2 mol, relative to 1 mol of the 7-amino comound (II). The reaction is conducted within the temperature range of -80 to 80°C, preferably -40 to 50°C, most preferably -30 to 30°C. The reaction time varies with kinds of the 7-amino compound (II) and carboxylic acid R b OH or a salt or reactive derivative thereof, kinds of the solvent (mixture ratio as well when mixture solvents are used) and reaction temperatures, but it is usually within the range from one minute to 72 hours, preferably from 15 minutes to three hours. When an acid halide is employed as the acylating agent, the reaction can be conducted in the presence of a deacidifying agent for the purpose of eliminating from the reaction system the hydrogen halogenide to be liberated. The deacidifying agent may be exemplified by inorganic bases such as sodium carbonate, potassium carbonate, calcium carbonate or sodium hydrogen carbonate; tertiary amines such as triethylamine, tri(n-propyl)amine, tri(n-butyl)amine, diisopropylethylamine, cyclohexyldimethylamine, pyridine, lutidine, γ-collidine, N,N-dimethylaniline, N-methylpiperidine, N-methylpyrrolidine or N-methylmorpholine; or alkylene oxides such as propylene oxide or epichlorohydrin. The 7-amino compound (II) can be synthesized by reacting a compound of the formula (wherein the symbol R⁵ stands for hydroxyl group, acyloxy group, carbamoyloxy group, substituted carbamoyloxy or halogen atom, and other symbols are of respectively the same meanings as defined above) or a salt or ester thereof with an imidazole compound of the formula A' (A' means an optionally substituted imidazole forming a condensed ring at 2,3- or 3,4-position) or a salt thereof. The starting compound (IX) or a salt or ester thereof is a compound which can be easily produced by a conventional method or an analogous one thereto. As salts and esters of the compound (IX) can be also mentioned here the same ones as those of the compound (II). As the acyloxy group represented by the symbol R⁵, the above mentioned acyl ⁺ oxy group can be employed also here, especial acyl ly preferable being acetoxy, chloroacetoxy, propionyloxy, butyryloxy, pivaloyloxy, 3-oxobutyryloxy, 4-chloro-3-oxobutyryloxy, 3-carboxypropionyloxy, 4-carboxybutyryloxy, 3-ethoxycarbamoylpropionyloxy, benzoyloxy, o-carboxy-benzoyloxy, o-(ethoxycarbonylcarbamoyl)benzoyloxy and o-(ethoxycarbonylsulfamoyl)benzoyloxy. As the substituted carbamoyloxy group represented by the symbol R⁵, the above mentioned ones can be employed also here, especially preferable being methylcarbamoyloxy and N,N-dimethylcarbamoyloxy. Halogen atoms represented by the symbol R⁵ are preferably chlorine, bromine and iodine. As to the imidazole compound A' and its salt, detailed description will be given hereafter. Even in case where the amino group at the 7-position is protected, the above reaction proceeds likewise. When desired, the protecting group may be removed after the reaction to thereby give a 7-amino compound (II). The carboxylic acid (R b OH) or a salt or reactive derivative thereof can be easily prepared by a known process or a process analogous thereto. Production method (2) Furthermore, the compound (I) can be synthesized by reacting a compound of the formula wherein R⁵ is hydroxyl group, acyloxy group, carbamoyloxy group, substituted carbamoyloxy group or halogen atom and other symbols are of the same meaning as defined above or a salt or ester thereof with an imidazole compound of the formula A' (A' means an optionally substituted imidazole forming a condensed ring at the 2,3- or 3,4-position) or a salt thereof. In this reaction imidazole compound A' or a salt thereof is reacted with a compund (X) or a salt or ester thereof (the compound (X), and salt and ester thereof may simply be abbreviated hereinafter as the compound (X)) to cause nucleophilic substitution, thereby to give the compound (I). In the compound (X), R⁵ stands for, also here, hydroxyl group, acyloxy group, carbamoyloxy group, substituted carbamoyloxy group or halogen atom. The compound (X) can be used in the free state or as salts or esters thereof. The salts and esters of the compound (X) are those mentioned as salts and esters of the 7-amino compound (II) in the above Production Method(1). The compound (X), or a salt and ester thereof can be easily prepared by known methods or analogous ones thereto. On the other hand, the imidazole compound A' stands for an optionally substituted imidazole forming a condensed ring at the 2,3-position or the 3,4-position. The condensed ring means a form of condensation between the imidazole ring and the 5- to 6-membered aromatic heterocyclic ring. Such condensed ring may be further condensed with another aromatic ring or aromatic heterocyclic ring. The optinally substituted imidazole (A') forming a condensed ring at the 2,3-position or the 3,4-position may be represented by the general formula [A 1' ] or [A 2' ]; and the A ⊕ group of the compound (I) to be synthesized by allowing the compound (X) to react with the compound [A 1' ] or a salt thereof stands for the afore-mentioned A¹ group, and the A ⊕ group of the compound (I) to be synthesized by allowing the compound (X) to react with the compound [A 2' ] or a salt thereof stands for the afore-mentioned A² group. The symbol B in the formulae of condensed imidazole [A 1' ] and [A 2' ] is of the same meaning as that of symbol B in the [A ¹ ] and [A ² ] groups defined in the above, Hence, the compound [A 1' ] is exemplified by and the compound [A 2' ] is exemplified by The substituents R 11' and R 12' on the imidazole compound A' are those mentioned as the substituents R¹¹ and R¹² of the group A. And, in the compound [A 1' ], the 5,6-position of the imidazole ring may be condensed with an alicyclic ring, aromatic ring or heterocyclic ring, which may be exemplified by In the above, B and R 12' are of the same meaning as defined in the foregoing. The above-mentioned substituents R 11' and R 12' may be further substituted. The imidazole compound A' may be used as salts thereof, which may be exemplified by inorganic acid addition salts, e.g. hydrochloride, hydrobromide, sulfate, nitrate or phosphate, or organic acid addition salts, e.g. formate, acetate, trifluoroacetate, methansulfonate or p-toluenesulfonate. The imidazole compound A' and its salt may be synthesized, in general, by known methods described in literature references or by analogous methods thereto. The nucleophilic substitution to the compound (X) with the imidazole compound A' or a salt thereof is a per se known reaction, which is usually conducted in a solvent, for example ethers, esters, halogenated hydrocarbons, hydrocarbons, amides, ketones, nitriles or water, which are used in the Production Method (1). Besides, alcohols such as methanol, ethanol, n-propanol, isopropanol, ethylene glycol or 2-methoxyethanol may be used as well. When the imidazole compound A' or a salt thereof is in liquid state, it may be sometimes used in a large excess amount (e.g. 10 to 200 mol) relative to the compound (X) to allow it to act also as the solvent. In this case, use of the above-mentioned solvents is unnecessary, or the imidazole A' or a salt thereof may be used as a mixture solvent with any of the above-mentioned solvents. The case where R⁵ stands for acyloxy group, carbamoyloxy group or a substituted carbamoyloxy group: Preferable solvents are water and mixture solvents of water-miscible organic solvents and water. Among the water-miscible organic solvents, preferable ones are exemplified by acetone, methyl ethyl ketone and acetonitrile. The amount of the nucleophilic reagent A' or a salt thereof is usually about 1 to 5 moles, preferably about 1 to 3 moles, relative to 1 mole of the compound (X) The reaction is conducted within a temperature ranging from about 10°C to 100°C, preferably from about 30 to 80°C. The reaction time depends on the kinds of the compound (X) and the compound A' or a salt thereof, kinds of solvents (mixture ratios when mixture solvents are used), or reaction temperature, and ranges usually from 30 minutes to five days, preferably from one hour to five hours. The reaction is advantageously conducted at pH 2 to 8, preferably near neutral pH, i.e. pH 5 to 8. The reaction readily proceeds usually in the presence of 2 to 30 equivalents of an iodide or thiocyanate. These salts are exemplified by sodium iodide, potassium iodide, sodium thiocyanate and potassium thiocyanate. In addition to the above exemplified salts, a surface-active quaternary ammonium salt such as trimethylbenzylammonium bromide, triethylbenzylammonium bromide or triethylbenzylammonium hydroxide may be sometimes used for allowing the reaction to proceed smoothly. The case where R⁵ stands for hydroxyl group The reaction may be conducted in the presence of an organic phosphorus compound according to the manner described in, for example, Publication of Unexamined Patent Application (Kokai) in Japan No. Sho 58-43979. The organic phosphorus compound is exemplified by o-phenylene phosphorochloridate, o-phenylene phosphorfluoridate, methyl o-phenylene phosphate, ethyl o-phenylene phosphate, propyl o-phenylene phosphate, isopropyl o-phenylene phosphate, butyl o-phenylene phosphate, isobutyl o-phenylene phosphate, sec.-butyl o-phenylene phosphate, cyclohexyl o-phenylene phosphate, phenyl o-phenylene phosphate, p-chlorophenyl o-phenylene phosphate, p-acetylphenyl o-phenylene phosphate, 2-chloroethyl o-phenylene phosphate, 2,2,2-tri chloroethyl o-phenylene phosphate, ethoxycarbonylmethyl o-phenylene phosphate, carbamoylmethyl o-phenylene phosphate, 2-cyanoethyl o-phenylene phosphate, 2-methylsulfonylethyl o-phenylene phosphate, benzyl o-phenylene phosphate, 1,1-dimethyl-2-propenyl o-phenylene phosphate, 2-propenyl o-phenylene phosphate, 3-methyl-2-butenyl o-phenylene phosphate, 2-thienylmethyl o-phenylene phosphate, 2-furfurylmethyl o-phenylene phosphate, bis-o-phenylene pyrophosphate, 2-phenyl-1,3,2-benzodioxaphosphole-2-oxide, 2-(p-chlorophenyl)-1,3,2-benzodioxaphosphole-2-oxide, 2-butyl-1-3,2-benzodioxaphosphole-2-oxide, 2-anilino-1,3,2-benzodioxaphosphole-2-oxide, 2-phenylthio-1,3,2-benzodioxaphosphole-2-oxide, 2-methoxy-5-methyl-1,3,2-benzodioxaphosphole-2-oxide, 2-chloro-5-ethoxycarbonyl-1,3,2-benzodioxaphosphole-2-oxide, 2-methoxy-5-ethoxycarbonyl-1,3,2-benzodioxaphosphole-2-oxide, 5-ethoxycarbonyl-2-phenyl-1,3,2-benzodioxaphosphole-2-oxide, 2,5-dichloro-1,3,2-benzodioxaphosphole-2-oxide, 4-chloro-2-methoxy-1,3,2-benzodioxaphosphole-2-oxide, 2-methoxy-4-methyl-1,3,2-benzodioxaphosphole-2-oxide, 2,3-naphthalenemethyl phosphate, 5,6-dimethyl-2-methyloxy-1,3,2-benzodioxaphosphole-2-oxide, 2,2-dihydro-4,5,6,7-tetrachloro-2,2,2-trimethoxy-1,3,2-benzodioxaphosphole, 2,2-dihydro-4,5,6,7-tetrachloro-2,2,2-triphenoxy-1,3,2-benzodioxaphosphole, 2,2-dihydro-2,2-ethylenedioxy-2-methoxy-1,3,2-benzodioxaphosphole, 2,2-dihydrobenzyl-2,2-dimethoxy-1,3,2-benzodioxaphosphole, 2,2-dihydro-4,5-benzo-2,2,2-trimethoxy-1,3,2-benzodioxaphosphole, 2,2-dihydro-2,2,2,-triphenoxy-1,3,2-benzodioxaphosphole, 2,2-dihydro-2,2-(o-phenylenedioxy)-2-phenoxy-1,3,2-benzodioxaphosphole, 2-chrolo-2,2-dihydro-2,2-(o-phenylenedioxy)-1,3,2-benzodioxaphosphole, 2,2-dihydro-2-methoxy-2,2-(o-phenylenedioxy)-1,3,2-benzodioxaphosphole, 2,2-dihydro-2,2,2-trichloro-1,3,2-benzodioxaphosphole, 9,10-phenanthrenedioxytrimethoxyphosphorus, o-phenylene phosphorochloridite, o-phenylene phosphorobromidite, o-phenylene phosphorofluoridite, methyl o-phenylene phosphite, butyl o-phenylene phosphite, methoxycarbonylmethyl o-phenylene phosphite, phenyl o-phenylene phosphite, p-chloro (or p-nitro)phenyl o-phenylene phosphite, 2-phenyl-1,3,2-benzodioxaphosphole, bis-o-phenylene pyrophosphite, 2-methoxy-5-methyl-1,3,2-benzodioxaphosphole, 5-acetyl-2-phenoxy-1,3,2-benzodioxaphosphole, 9,10-phenanthrene phosphorochloridite, 2-chloro-4-methyl-1,3,2-benzodioxaphosphole, 5-ethoxycarbonyl-2-phenyl-1,3,2-benzodioxaphosphole, 2-chloro-2-thioxo-1,3,2-benzodioxaphosphole, 2-phenoxy-2-oxo-1,3,2-benzodiazaphosphole, 2-phenoxy-1,3,2-benzodioxaazaphosphole, 2,2-dihydro-2-oxo-2-methoxy-4,5-dimethyl-1,3,2-dioxaphosphole, 2,2-dihydro-2-oxo-2-chloro-4,5-dimethyl-1,3,2-dioxaphosphole, 2,2-dihydro-2-oxo-2-(1-imidazolyl)-4,5-dimethyl-1,3,2-dioxaphosphole, 2,2-dihydro-2,2-ethylenedioxy-2-methoxy-4,5-dimethyl-1,3,2-dioxaphosphole, 2,2-dihydro-2,2-dimethoxy-2-phenoxy-4,5-dimethyl-1,3,2-dioxaphosphole, 2,2-dihydro-2,2,2-trimethoxy-4,5-dimethyl-1,3,2-dioxaphosphole, 2,2-dihydro-2,2,2-triphenoxy-4,5-dimethyl-1,3,2-dioxaphosphole, 2,2-dihydro-2,2,2-triethoxy-4,5-diphenyl-1,3,2-dioxaphosphole, 2,2-dihydro-2,2,2-trimethoxy-4,5-diphenyl-1,3,2-dioxaphosphole, 2,2-dihydro-2-oxo-2-methoxy-4,5-diphenyl-1,3,2-dioxaphosphole, 2,2-dihydro-2,2,2-trimethoxy-1,3,2-dioxaphosphole, 2,2-dihydro-2,2,2-trimethoxy-4-phenyl-1,3,2-dioxaphosphole, 2,2-dihydro-2,2,2-trimethoxy-4-methyl-1,3,2-dioxaphosphole, 2,2-dihydro-2,2,2-trimethoxy-4-methyl-5-phenylcarbamoyl-1,3,2-dioxaphosphole, 2,2,4,5,6,7-hexahydro-2,2,2-trimethoxy-1,3,2-benzodioxaphosphole, 2,2'-oxybis(4,5-dimethyl-2,2-dihydro-1,3,2-dioxaphosphole) and 2,2'-oxybis(4,5-dimethyl-2,2-dihydro-1,3,2-dioxaphosphole-2-oxide). For the reaction, any solvent can be emloyed if only it does not hamper the reaction, and, preferably, the afore-mentioned ethers, esters, halogenated hydrocarbons, hydrocarbons, amides, ketones, and nitriles may be used singly or in a mixture thereof. Especially, use of dichloromethane, acetonitrile, formamide, a mixture of formamide and acetonitrile, or a dichloromethane and acetonitrile brings about a preferable result. The amounts of the nucleophilic reagent A' or a salt thereof and the organic phosphorus compound are respectively, relative to 1 mole of the compound (X), about 1 to 5 moles and about 1 to 10 moles, more preferably about 1 to 3 moles and about 1 to 6 moles. The reaction is conducted within the temperature range from about -80°C to 50°C, preferably from about -40 to 40°C. The reaction time is usually within the range of one minute to 15 hours, preferably five minutes to two hours. To the reaction system may be added an organic base. The organic base may be exemplified by amines such as triethylamine, tri-(n-butyl)amine, di-(n-butyl)amine, diisobutylamine, dicyclohexylamine or 2,6-lutidine. The amount of the base to be added is preferably about 1 to 5 moles relative to 1 mole of the compound (X). The case where R⁵ stands for halogen atom: Preferable solvents are the afore-mentioned ethers, esters, halogenated hydrocarbons, hydrocarbons, amides, ketones, nitriles, alcohols and water. The amount of the nucleophilic reagent A' or a salt thereof to be used is usually, relative to one mole of the compound (X), about 1 to 5 moles, preferably about 1 to 3 moles. The reaction is conducted within a temperature range of about 0 to 80°C, preferably about 20 to 60°C. The reaction time is usually 30 minutes to 15 hours, preferably 1 to 5 hours. For accelerating the reaction, the reaction may be conducted in the presence of a dehalogenating agent. As such dehalogenating agents, there may be counted deacidifying agents such as inorganic bases, tertiary amines and alkylene oxides mentioned in the Production Method (1), while the nucleophilic reagent A' itself or a salt thereof may be allowed to act as the dehalogenating agent also. In this case, the compound A' or a salt thereof is used in an amount of two moles or more relative to one mole of the compound (X). The halogen atom shown by R⁵ is exemplified by chlorine, bromine and iodine, and preferably iodine. The compound (X) wherein R⁵ stands for iodine can be easily produced in accordance with the method described in, for example, Publication of Unexamined Patent Application (Kokai) in Japan No. Sho 58-57390 or a method analogous thereto. The compound (X) can be easily prepared by a known method or a method analogous thereto. Production method (3) The compound (I) (wherein R³ stands for an optionally substituted hydrocarbon residue) (this compound is referred to as the compound (I') or a salt or ester thereof) can also be prepared by, besides the above-mentioned Production Method (1) or (2), the production Method (3) to be described below. The reaction scheme is as follows: wherein the symbol R 3'' stands for an optionally substituted hydrocarbon residue, and the symbols Z, R¹, R⁴, R¹³ and A are of the same meaning as defined above. This is a method of synthesizing the compound (I') or a salt or ester thereof (the compound (I') and salt and ester thereof may simply be abbreviated hereinafter as the compound (I')) by reacting a compound of the formula: R 3'' OH or a reactive derivative thereof with a hydroxyimino compound (V) or a salt or ester thereof (the compound (V) and salt and ester thereof may simply be abbreviated hereinafter as the hydroxyimino compound (V)), which is a per se known etherifying reaction. R 3'' stands for an optionally substituted hydrocarbon residue which is the same as that referred to in R³. R 3'' OH may be employed as it is or as a reactive derivative thereof. Reactive derivatives of R 3'' OH are represented by the formula R 3'' Y, having a group to be liberated together with the hydrogen atom of the hydroxyimino compound (V). The group Y to be liberated together with a hydrogen atom may be exemplified by halogen atom, sulfo group or mono-substituted sulfonyloxy group. The halogen atom may be exemplified by chlorine, bromine or iodine. The mono-substituted sulfonyloxy group may be exemplified by C₁₋₆ alkylsulfonyloxy and C₆₋₁₀ arylsulfonyloxy groups, e.g. methanesulfonyloxy, ethanesulfonyloxy, benzenesulfonyloxy or p-toluenesulfonyloxy. When a C₁₋₄ alkylether derivative of the compound (V) is intended, there may be used, besides the above-mentioned reaction derivatives, C₁₋₄ diazoalkane such as diazomethane or diazoethane, and di-C₁₋₄ alkyl sulfate such as dimethyl sulfate or diethyl sulfate. The compound (V) can be prepared by the acylation as mentioned above in the Production Method (1) or the nucleophilic substitution as mentioned above in the Production Method (2). The reaction schema are as follows, respectively: The starting materials (XII) and (X') can be easily prepared by a known method or an analogous one thereto. The compound R 3'' OH and the reactive derivative thereof can also be easily prepared by a known method or an analogous one thereto. The detailed condition of the reaction of the Method (3) is as follows: (3-1) The case where R 3'' OH is used: By using a suitable dehydrating agent the hydroxyimino compound (V) is reacted with the compound R 3'' OH to synthesize a compound (I'). The dehydrating agent may be exemplified by phosphorous oxychloride, thionyl chloride, dialkyl azodicarboxylate (usually used in the presence of phosphine) or N,N-dicyclohexylcarbodiimide, and preferably diethyl azodicarboxylate in the presence of triphenyl phosphine. The reaction in which diethyl azodicarboxylate is used in the presence of triphenyl phosphine is usually conducted in an anhydrous solvent such as ethers or hydrocarbons mentioned above. Relative to 1 mole of the compound (V), about 1 to 1.5 mole each of the compound R 3'' OH, ethyl azodicarboxylate and triphenyl phosphine is employed. The reaction requires 1 to 4 days at a temperature range of about 0 to 50 °C. (3-2) The case where R 3'' Y is used: The reaction between R 3'' Y and a hydroxyimino compound (V) is a conventional etherification reaction, which is conducted in a solvent. The solvent is exemplified also here by those as mentioned in the Production Method (1) above, i.e. ethers, esters, hydrogenated hydrocarbons, hydrocarbons, amides, ketones, nitriles, alcohols, water or a mixture of any of them, preferably a mixture solvent of a water-miscible solvent and water (e.g. aqueous methanol, aqueous ethanol, aqueous acetone and aqueous dimethyl sulfoxide). The reaction may also be allowed to proceed smoothly in the presence of a suitable base. The base may be exemplified by inorganic bases such as alkali metal salts e.g. sodium carbonate, sodium hydrogencarbonate or potassium carbonate, or alkali metal hydroxides e.g. sodium hydroxide or potassium hydroxide. This reaction may be conducted in a buffer solution of pH 7.5 to 8.5. The mole numbers of a reagent R 3'' Y and the base relative to 1 mole of the starting compound (V) are respectively about 1 to 5 and about 1 to 10, preferably about 1 to 3 and about 1 to 5, respectively. The reaction temperature is in the range from about -30°C to 100°C, preferably about O°C to 80°C. The reaction time ranges from 10 minutes to 15 hours, preferably from 30 minutes to 5 hours. (3-3) The case where C₁₋₄ diazoalkane is used: The reaction is usually conducted in a solvent. As the solvent are employed, for example, the afore-mentioned ethers and hydrocarbons. The hydroxyimino compound (V) is dissolved in a solvent, to which is then added a solution of a diazoalkane compound, whereupon the reaction proceeds. The reagent is used, relative to 1 mole of the compound (V), in an amount of about 1 to 10 moles, preferably about 1 to 5 moles. The reaction is conducted at a relatively low temperature range of from about -50°C to 20°C, preferably from about -30°C to 0°C. The reaction time ranges from 1 minute to 5 hours, preferably 10 minutes to one hour. (3-4) The case where di-C₁₋₄ alkylsulfate is used: The reaction is conducted usually in water or a mixture solvent of a water-miscible solvent and water. As the mixture solvent are mentioned those mentioned in the Production Method (3-2). This reaction is usually conducted in the presence of an inorganic base, for example, an alkali metal hydroxide such as sodium hydroxide and potassium hydroxide. The reagent is used in an amount of about 0.5 to 10 moles, preferably about 1 to 2 moles, relative to 1 mole of the compound (V). The reaction temperature ranges from about 20 to 100°C, preferably from about 50°C to 100°C. The reaction time ranges from 10 minutes to 5 hours, preferably from 30 minutes to 3 hours. After the above mentioned Production Method (1) - (3), when required, removal of protecting groups and purification are conducted to obtain the compound (I) of this invention. Methods of removing protecting groups and purification are described as follows: Process of removing protecting group: As afore-mentioned, in the fields of β-lactam and peptide syntheses, amino-protecting groups have been sufficiently studied, and the method of protecting and deprotecting amino groups has been established. The method of removing the amino-protecting group has also been established, and, in the present invention as well, for removing protecting groups, conventional technique can be used as such. For example, monohalogenoacetyl group (chloroacetyl, bromoacetyl, etc.) can be removed by using thiourea; alkoxycarbonyl group (methoxycarbonyl, ethoxycarbonyl, tert-butoxycarbonyl, etc.) can be removed by using an acid (e.g. hydrochloric acid); aralkyloxycarbonyl group (e.g. benzyloxycarbonyl, p-methylbenzyloxycarbonyl or p-nitrobenzyloxycarbonyl) can be removed by means of catalytic reduction; and 2,2,2-trichloroethoxycarbonyl can be removed by using zinc and an acid (e.g. acetic acid). On the other hand, in the case when the compound (I) as the intermediate has been esterified, the ester residue can be removed by a per se known process or an analogous one thereto. For example, 2-methylsulfonylethyl ester can be removed by using an alkali; aralkyl ester (benzyl ester, p-methoxybenzyl ester, p-nitrobenzyl ester, etc.) can be removed by using an acid (e.g. trifluoroacetic acid) or by means of catalytic reduction; 2,2,2-trichloroethyl ester can be removed by using zinc and an acid (e.g. acetic acid); and silyl ester (e.g. trimethylsilyl ester or tert-butyldimethylsilyl ester) can be removed by using only water. Process of purifying the compound (I): The compound (I) produced in the reaction mixture by any of the processes described in detail in the foregoing Production Methods (1)-(3) and, upon necessity, followed by removal of protecting groups by conducting the above-mentioned process, can be isolated and purified by a known process such as extraction, column-chromatography, precipitation and recrystallization. On the other hand, the compound (I) thus isolated can be converted into then desired physiologically acceptable salts or bioavailably unstable non-toxic esters. The sulfoxide ((I), Z = S → O) of the cephem compound ((I), Z=S) can be prepared by subjecting the compound ((I),Z=S) to a conventional oxidation. Oxidizing agents suitable for oxidation of the sulfur atom of the cephem ring are exemplified by oxygen, peracid, hydroperoxide, or hydrogen peroxide, and the peracid may be made by mixing an acid with a peroxide in the reaction system of the oxidation. As such peracids, use is often made of peracetic acid, perbenzoic acid or p-chloroperbenzoic acid. The reaction is usually conducted in a solvent which is exemplified by ethers such as dioxane or tetrahydrofuran; halogenated hydrocarbons such as dichloromethane, chloroform or chlorobenzene; organic acids such as formic acid, acetic acid, trifluoroacetic acid; or amides such as dimethylformamide or dimethylacetamide. The reaction temperature ranges from about -20°C to 80°C, and preferably a temperature as low as possible, i.e. ranging from about -20°C to 20°C. It is generally known that, when the cephem compound ((I), Z=S) is subjected to oxidation, sulfoxide having an S-configuration is produced. The R- and S-sulfoxide can be separated by utilizing the difference in solubility between them or the difference in travelling rate in chromatography. The above-mentioned oxidation to give sulfoxide can be conducted before or after the aforementioned. Production Methods (1)-(4) The compound (I) of this invention can be administered orally or non-orally as injections, capsules, tablets or granules, like known penicillin and cephalosporin preparations. The dosage is 0.5 to 80 mg/day, preferably 1 to 20 mg/day in 3 to 4 doses relative to one kilogram of the body weight of men and animals infected with pathogenic bacteria as set forth above. Carriers of injectable preparations are exemplified by distilled water or physiological saline solution: When used as capsule, powder, granule or tablet, the compound (I) is mixed with conventional pharmaceutically acceptable excipients (e.g. starch, maltose, sucrose, calcium carbonate or calcium phosphate), binders (e.g. starch, gum-arabica, carboxymethylcellulose, hydroxypropylcellulose or crystalline cellulose), lubricants (e.g. magnesium stearate or talc) and disintegrators (e.g. carboxymethyl calcium or talc). The present invention will be further explained by the following Reference Examples and Examples, but those Examples are mere examples and do not restrict the present invention in any manner. Elution in column-chromatography in the Reference Examples and Examples was conducted under observation by means of TLC (Thin-Layer Chromatography), wherein were employed 60F₂₅₄® manufactured by E. Merck (West Germany) as TLC plate, the solvent for elution in the column-chromatography as developing solvent, and a UV detector as detecting means. As silica-gel for the column, Kieselgel 60® (70-230 mesh) manufactured by E. Merck (West Germany) was employed. Sephadex R is a product of Pharmacia Fine Chemicals (Sweden). XAD-2® resin is a product of Rohm & Haas Co. (U.S.A.). NMR spectrum was determined by XL-100A (100 MHz)-, EM390 (90 MHz)-, EM360 (60MHz)-, or T₆₀ (60 MHz)-type spectrometer using tetramethylsilane as internal or external standard, and all the delta values were shown by ppm. The numeral values parenthesised for mixture solvents mean the ratios by volume of each solvent mixed. "%" for solvents means number of grams in 100 ml of each solution. Symbols in the Reference Examples and Examples have respectively the meanings as follows: s: singlet d: doublet t: triplet q: quartet ABq: AB type quartet d. d: double doublet m: multiplet br.: broad J: coupling constant Hz: Herz mg: milligram g: gram ml: milliliter ℓ or l: liter %: percent DMSO: dimethylsulfoxide D₂O: deuterium oxide CDCl₃: deuterochloroform Reference Example 1 7β-[2-(5-tert-butoxycarbonylamino-1,2,4-thiadiazol-3-yl)-2(Z)-methoxyiminoacetamido]-3-(3-oxobutyryloxymethyl)-3-cephem-4-carboxylic acid To 4 ml of dichloromethane is added 302 mg of 2-(5-tert-butoxycarbonylamino-1,2,4-thiadiazol-3-yl)-2(Z)-methoxyiminoacetic acid, followed by addition of 208 mg of phosphorous pentachloride. The mixture is stirred with ice-cooling for 15 minutes. The solvent is then evaporated off under reduced pressure and hexane is added to the residue. The mixture is evaporated to dryness under reduced pressure and the residue is dissolved in dichloromethane. The resulting solution is added to a solution of 300 mg of 7β-amino-3-(3-oxobutyloxymethyl)-3-cephem-4-carboxylic acid and 0.6 ml of triethylamine in 5 ml of dimethylacetamide, and the mixture is stirred with ice-cooling for 30 minutes. To the reaction mixture is added a solution of 1 g of phosphoric acid in 10 ml of water and the resulting mixture is extracted with methyl ethyl ketone (10 ml). The extract is washed with water and dried over magnesium sulfate. The solvent is then evaporated off under reduced pressure. Ethyl acetate is added to the residue and the solvent is evaporated again to give 390 mg of the above-identified compound. 2980, 2940, 1780, 1715, 1540, 1370, 1245, 1150, 1040, 855. NMR spectrum (d₆-DMSO) δ : 1.56(9H,s), 2.20(3H,s), 3.43 and 3.70 (2H,ABq,J=18Hz), 3.65(2H,s), 4.00(3H,s), 4.80 and 5.12 (2H,ABq,J=12Hz), 5.18(1H.d,J=4.5Hz), 5.88(1H,d.d, J=9Hz and 4.5Hz), 9.63(1H,d,J=9Hz). Reference Example 2 7β-[2-(5-Amino-1,2,4-thiadiazol-3-yl)-2(Z)-ethoxyiminoacetamido]-3-(3-oxobutyryloxymethyl)-3-cephem-4-carboxylic acid In 200 ml of dichloromethane is suspended 11 g of 7β-amino-3-(3-oxobutyryloxymethyl)-3-cephem-4-carboxylic acid. To the suspension is added 14 g of bistrimethylsilylacetamide and the mixture is stirred at room temperature until complete dissolution and cooled in an ice-water bath. To this solution, 14 g of 2-(5-amino-1,2,4-thiadiazol-3-yl)-2(Z)-ethoxyiminoacetyl chloride is added and the mixture is stirred for a while, to which 6 g of dimethylacetamide is added. The whole mixture is stirred with ice-cooling for 60 minutes. The dichloromethane is evaporated off and the residue is dissolved in methyl ethyl ketone. The solution is washed with water and dried. The solvent is then evaporated off and diethyl ether is added to the residue to give a fine percipitate, which is collected by filtration, giving 12.5 g of the above-identified compound. 3300, 3000, 1780, 1720, 1620, 1520, 1410, 1260, 1150, 1040. NMR spectrum (d₆-DMSO) δ : 1.25(3H,t,J=7Hz), 2.18(3H,s), 3.41 and 3.63(2H,ABq,J=18Hz), 3.62(2H,s), 4.18(2H,q,J=7Hz), 4.76 and 5.06(2H,ABq,J=13Hz), 5.14(1H,d,J=4.8Hz), 5.82 (1H,d.d,J=8Hz and 4.8Hz), 8.00(2H,br), 9.48(1H,d,J=8Hz). Reference Example 3 7β-[2-(5-Amino-1,2,4-thiadiazol-3-yl)-2(Z)-(cyanomethoxyimino)acetamido]-3-(3-oxobutyryloxymethyl)-3-cephem-4-carboxylic acid A mixture of 13 g of 2-(5-amino-1,2,4-thiadiazol-3-yl)acetic acid, 10.7 g of selenium dioxide and 200 ml of dioxane is heated in an oil bath kept at 90°C for 40 minutes with stirring. After cooling, dioxane is evaporated off. To the residue is added 150 ml of ethyl acetate and, after filtration, ethyl acetate is evaporated off under reduced pressure. To the residue are added 100 ml of ethanol and then, with stirring, 3.6 g of O-cyanomethylhydroxylamine. The mixture is then stirred at room temperature for 40 minutes and ethanol is evaporated off under reduced pressure. The residue is dissolved in 150 ml of ethyl acetate. The ethyl acetate solution is washed once with water and then shaken with 100 ml of 5 % aqueous sodium bicarbonate solution. The aqueous phase is separated, covered with 150 ml of ethyl acetate and acidified with phosphoric acid with efficient stirring. The ethyl acetate layer is separated and dried over anhydrous magnesium sulfate. Ethyl acetate is evaporated off under reduced pressure and the residue is dissolved in 30 ml of dichloromethane. To the resulting solution is added 2.2 g of phosphorous pentachloride under ice-cooling. After 20 minutes, stirring at the same temperature, dichloromethane is evaporated off. The residue is redissolved in 5 ml of dichloromethane and the solution is added all at once to a solution composite of 3.1 g of 7β-amino-3-(3-oxobutyryloxymethyl)-3-cephem-4-carboxylic acid, 6 ml of bistrimethylsilylacetamide and 60 ml of dichloromethane and the mixture is stirred under ice-cooling for 30 minutes. Dichloromethane is then evaporated off and the residue is dissolved in 100 ml of ethyl acetate. The resulting solution is washed with water and dried over anhydrous magnesium sulfate and ethyl acetate is then evaporated off under reduced pressure. To the residue is added 10 ml of ice-cooled trifluoroacetic acid and the mixture is stirred at room temperature for 30 minutes. To the reaction mixture is added 50 ml of ethyl acetate and the solvent is then evaporated under reduced pressure. The residue is triturated with ethyl acetate and the insoluble substance is collected by filtration giving 2 g of crude above-identified compound. The filtrate is then concentrated, the residue treated with diethyl ether and insoluble substance is collected by filtration to give 1.4 g of the above-identified compound. 1780, 1700, 1620, 1520, 1400, 1360, 1310, 1140, 1040. NMR spectrum (d₆-DMSO) δ : 2.21(3H,s), 3.44 and 3.68(2H,ABq, J=18Hz), 3.65(2H,s) 4.79 and 5.10(2H,ABq,J=14Hz), 5.11 (2H,s), 5.17(1H,d,J=4.8Hz), 5.85(1H, d.d,J=4.8 and 8Hz), 8.16(2H,br.), 9.74(1H,d,J=8Hz). Reference Example 4 Imidazo[1,2-a]pyridine derivatives, imidazo[1,5a]pyridine derivatives and imidazo[1,2-b]pyridazine derivatives are prepared according to the known methods described in e.g. J. Org. Chem. 30 , 4081 (1965), J. Org. Chem., 30 , 4085 (1965), J. Heterocyclic Chem., 2 , 53 (1965), Tetrahedron, 23 , 387 (1967), Tetrahedron, 24 , 239 (1968), J. Org. Chem., 30 , 2403 (1965), J. Med. Chem., 12 , 122 (1969) and the similar methods. Synthesis of novel imidazo[1,2-a]pyridine derivatives is described below. 4-1) 6-Cyanoimidazo[1,2-a]pyridine A mixture of 2.6 g of 6-carbamoylimidazo[1,2-a]pyridine and 30 ml of phosphorous oxychloride is heated under reflux for 16 hours. The excess phosphorous oxychloride is removed under reduced pressure and the residue is poured onto ice. The mixture is neutralized with sodium carbonate and extracted with ethyl acetate. The organic layer is washed with saturated aqueous sodium chloride solution and dried over anhydrous magnesium sulfate. The solvent is then evaporated off under reduced pressure to give 2.0 g of the above-identified compound as colorless crystals. M.p.: 166-167°C Elemental analysis for C₈H₅N₃: Calcd. (%): C, 67.13; H, 3.52; N, 29.35. Found (%): C, 67.37; H, 3.62; N, 28.99. 4-2) 8-Hydroxyimidazo[1,2-a]pyridine hydrochloride In 80 ml of concentrated hydrochloric acid is dissolved 5 g of 8-benzoyloxyimidazo[1,2-a]pyridine, and the solution is stirred at room temperature for 24 hours and then concentrated. After addition of 1-butanol, water is azeotropically removed by distillation, and the residue is crystallized from diethyl ether to give 3.8 g of the above-identified compound. M.p.: 153-156°C 1670, 1580, 1520, 1410, 1320, 1300. NMR spectrum (d₆-DMSO) δ : 7.2-7.4(2H,m), 8.25(1H,d), 8.3-8.5(2H,m). Novel imidazo[1,2-b]pyridazine derivatives are prepared as follows. 4-3) 6-Ethoxyimidazo[1,2-b]pyridazine Sodium metal (0.55 g) is dissolved in 30 ml of ethanol and, to the solution, is added 3 g of 6-chloroimidazo[1,2-b]pyridazine and the mixture is heated under reflux for 3 hours. The solvent is then evaporated off under reduced pressure and the residue is dissolved in water and the mixture is extractedted with methylene chloride. The extracts are combined, washed with saturated solution of sodium chloride and dried over MgSO₄. The solvent is then evaporated to give 3.3 g of the title compound as colorless crystals. M.p.: 102-103°C NMR spectrum (CDCl₃) δ : 1.45(3H,t,J=7Hz), 4.53(2H,q,J=7Hz), 6.63(1H,d,J=10Hz), 7.56(1H,br.s), 7.68(1H,br.s), 7.74(1H,d,J=10Hz). 4-4) 6-Methylthioimidazo[1,2-b]pyridazine To a solution of 3.1 g of 6-chloroimidazo[1,2-b]pyridazine in 5 ml of dimethylformamide, 13 ml of 15 % aqueous solution of sodium methylmercaptide are added and the mixture is heated for 3 hours at 100-105°C with stirring. After cooling, the reaction mixture is diluted with water and extracted with ether. The extract is washed with water, saturated aqueous solution of sodium chloride and dried over MgSO₄. Evaporation of the solvent under reduced pressure gives 2.81 g of the title compound as colorless crystals. M.p.: 66-68°C NMR spectrum (CDCl₃) δ : 2.59(3H,s), 6.83(1H,d,J=10Hz), 7.63 (1H,s), 7.70(1H,d,J=10Hz), 7.85(1H,br.s). 4-5) 6-Dimethylamino[1,2-b]pyridazine 6-Chloroimidazo[1,2-b]pyridazine (2.8 g) and 50 ml of dimethylamine solution are placed in a sealed tube and heated for 5 hours at 180°C. After cooling, the solvent is evaporated off and the residue is dissolved in water. The mixture is made alkaline with 10 % aqueous sodium hydroxide solution and extracted with ether. The organic phase is separated, washed with water and then with saturated sodium chloride solution and dried over MgSO₄. Evaporation of the solvent gives 2.61 g of the title compound as pale yellow crystals. M.p.: 83-85°C NMR spectrum (CDCl₃) δ : 3.10(6H,s), 6.72(1H,d,J=10Hz), 7.53 (1H,br.s), 7.68(1H,br.s), 7.69(1H,d,J=10Hz). 4-6) 6-(2-Dimethylaminoethoxy)imidazo[1,2-b]pyridazine Sodium metal (0.25 g) and 6-chloroimidazo[1,2-b]pyridazine are added to 25 ml of 2-dimethylaminoethanol and the mixture is heated in a sealed tube for 3 hours at 130°C. After cooling, the solvent is evaporated and the residue is treated with water and extracted with methylene chloride. The organic layer is separated, washed with saturated sodium chloride solution and dried over MgSO₄. Evaporation of the solvent gives the title compound as a viscous oil which solidified on standing. The yield is 2.5 g. NMR spectrum (CDCl₃) δ : 2.37(6H,s), 2.78(2H,t,J=6Hz), 4.43 (2H,t,J=6Hz), 6.75(1H,d,J=10Hz), 7.60(1H,d,J=2Hz), 7.75(1H,d,J=2Hz), 7.80(1H,d,J=10Hz). 4-7) 6-(2-Dimethylaminoethylthio)imidazo[1,2-b]pyridazine To 20 ml of methanol is dissolved 2.8 g of 2-dimethylaminoethanethiol. To this, 20 mol of 2 M solution of sodium methoxide in methanol and 3 g of 6-chloroimidazo[1,2-b]pyridazine are added successively and the mixture is heated in a sealed tube for 4 hours at 150°C. After cooling, the solvent is evaporated and the residue is treated with water. The mixture is then extracted with methylene chloride. The organic layer is separated, washed with saturated aqueous solution of sodium chloride and dried over MgSO₄. Evaporation of the solvent gives 2.5 g of the title compound as pale yellow crystals. M.p.: 52-54°C NMR spectrum (CDCl₃) δ : 2.34(6H,s), 2.70(2H,t,J=7Hz), 3.37 (2H,t,J=7Hz), 6.83(1H,d,J=10Hz), 7.68(1H,br.s), 7.74 (1H,d,J=10Hz), 7.81(1H,br.s). 4-8) 6-Fluoroimidazo[1,2-b]pyridazine (1) A mixture of 3,6-difluoropyridazine (7.8 g) and 25 ml of concentrated ammonium hydroxide solution is heated in a sealed tube for 2 hours at 70°C. After cooling, the crystals separated are filtered and washed with water to give 4 g of 3-amino-6-fluoropyridazine. NMR spectrum (d₆-DMSO) δ : 6.23(2H,br.s), 7-7.2(2H,m). (2) A mixture of 16.6 g of bromoacetaldehyde diethylacetal, 7 ml of concentrated HBr solution and 7 ml of water is heated one hour at 100°C. After cooling, the mixture is diluted with 100 ml of ethanol and neutralized with NaHCO₃. Insoluble material is removed by filtration and to the filtrate is added 5 g of 3-amino-6-fluoropyridazine and the mixture is stirred overnight at room temperature. Crystals separated are filtered, washed with ether and dissolved in water. The solution is made alkaline by addition of sodium carbonate and extracted with methylene chloride. The organic layer is washed with water saturated with sodium chloride and dried over MgSO₄. Evaporation of the solvent gives 1.7 g of the title compound as pale yellow crystals. NMR spectrum (CDCl₃) δ : 6.90(1H,d,J=10Hz), 7.83(1H,s), 7.88 (1H,s), 7.95(1H,d,J=10Hz). Reference Example 5 7β-(t-Butoxycarbonylamino)-3-(3-oxobutyryloxymethyl)-3-cephem-4-carboxylic acid. To a mixture of 200 g of 7β-amino-3-(3-oxobutyryloxymethyl)-3-cephem-4-carboxylic acid in 500 ml of dimethylsulfoxide is added 129 g of triethylamine with stirring, followed by stirring at room temperature for 20 minutes. Then to the mixture is added 200 g of di-t-butyl dicarbonate at room temperature, followed by stirring at room temperature for 16 hours. To the mixture are added 200 g of ice, 2 l of water, and 1 l of ethyl acetate, and the aqueous layer is separated. To the aqueous solution are added 1 l of ethyl acetate and 129 g of phosphoric acid. After vigorous stirring, the ethyl acetate layer is separated and the aqueous layer is extracted with 1 l of ethyl acetate. The extracts are combined, washed with 2 l of ice water (twice) and saturated aqueous sodium chloride solution in that order and dried over magnesium sulfate. The ethyl acetate solution is concentrated under reduced pressure, followed by adding 100 ml of methylene chloride (this procedure is repeated three times). Resulting residue is dried over phosphorous pentoxide under reduced pressure to give 194 g of the title compound. Yield: 74 %. Elemental analysis for C₁₇H₂₂N₂O₈S . O.5H₂O Calcd. (%): C, 48.22; H, 5.47; N, 6.62. Found (%): C, 48.16; H, 5.30; N, 6.32. 1780, 1720, 1520, 1370, 1320 NMR(DMSO-d₆) δ : 1.42(9H,s), 2.18(3H,s), 3.41 and 3.62(2H, AB q ,J=18Hz), 3.62(2H,s), 4.78 and 5.06(2H,AB q ,J=14Hz), 5.03(1H,d,J=5Hz), 5.45(1H,d.d,J=5Hz and 8Hz), 7.83 (1H,d,J=8Hz). Reference Example 6 7β-Amino-3-[(imidazo[1,2-b]pyridazinium-1-yl)methyl]-3-cephem-4-carboxylate hydrochloride. (1) 7β-[D-5-Carboxy-5-phenoxycarbonylaminovaleramido]-3-hydroxymethyl-3-cephem-4-carboxylic acid di-(tri-butylamine) salt (25.9 g) and imidazo[1,2-b]pyridazine (7.15 g) are dissolved in 150 ml of methylene chloride. The solution is cooled to -50°C and to this, 30 ml of 2 M solution of ethyl O-phenylenephosphate in methylene chloride is added. The mixture is maintained at -50 to -40°C for two minutes and then warmed up gradually up to 5°C over 2 hours. A precipitate separates. Ethyl acetate (450 ml) is added to the reaction mixture and is filtered and washed twice with each 100 ml of methylene chloride and then three times with ethyl acetate to give 17.8 g of 7β-(D-5-carboxy-5-phenoxycarbonylaminovaleramido)-3-[imidazo[1,2-b]pyridazinium-1-yl)methyl]-3-cephem-4-carboxylate. Yield: 100 %. TLC (Silica gel, Merck, Art 5715; Solvent: acetonitrile: water = 4 : 1): Rf = 0.19. 1780, 1720, 1625, 1520, 1485, 1380, 1200. (2) The compound (5.95 g) obtained above is pulverized and added to 150 ml of methylene chloride. To this, under ice-cooling, 5.94 ml of tributylamine and 12.7 ml of dimethylaniline are added. Then, the resulting solution is cooled to -30°C and to this is added 8.7 ml of propionyl chloride. After being stirred for 15 minutes at -20°C to -10°C, the mixture is cooled to -60°C. To this, 7.29 g of phosphorous pentachloride is added all at once and the mixture is stirred for 50 minutes at -55°C to -50°C. Then, 30 ml of isobutanol is added to the reaction mixture maintaining the inner temperature at -55°C to -45°C. After completion of the addition, the reaction mixture is warmed up from -50°C to 20°C over about one hour and then stirred for half an hour at 20°C and for one hour at 0°C. The precipitate separated is collected by filtration and washed three times with each 10 ml of methylene chloride and dried giving 2.87 g of the title compound. Yield: 81 %. TLC (Silica gel, Merck, Art 5715; Solvent: acetonitrile: water = 4 : 1): Rf = 0.14 1780, 1720, 1625, 1485, 1380, 1200. Rerference Example 7 7β-Amino-3-[imidazo[1,2-b]pyridazinium-1-yl)methyl]-3-cephem-4-carboxylate hydrochloride. 7β-[D-5-Carboxy-5-phenoxycarbonylaminovaleramido]-3-hydroxy methyl-3-cephem-4-carboxylic acid di-(tributylamine) salt (51.8 g) and imidazo[1,2-b]pyridazine (14.3 g) are dissolved in 300 ml of methylene chloride and the resulting solution is cooled to -50°C. To this, is added 24.0 g of ethyl O-phenylenephosphate and the mixture is stirred for two minutes at -50°C to -40°C. Then, the mixture is warmed up from -40°C to 10°C over 2 hours. A precipitate separates. To the reaction mixture, 600 ml of methylene chloride and 28.6 ml of tributylamine are added at 0°C to redissolve the precipitate and then, after addition of 76 ml of dimethylaniline, cooled to -30°C. To this is added 52.1 ml of propionyl chloride and the mixture is stirred for 15 minutes at -20°C to -10°C and then cooled to -55°C. To this, 43.7 g of phosphorous pentachloride is added all at once and the mixture is stirred for 50 minutes at -55°C to -50°C. Then, 180 ml of isobutanol is added, maintaining the inner temperature between -55°C to -45°C. After completion of the addition, the mixture is warmed up from -50°C to 20°C over about one hour and then stirred for 30 minutes at 20°C and for one hour at 0°C. The precipitate separated is collected by filtration and washed three times with each 50 ml of methylene chloride and dried to give 20.0 g of the title compound. Yield: 94.2 %. TLC (Silica gel, Merck, Art 5715; Solvent: acetonitrile : water = 4 : 1): Rf = 0.14. Reference Example 8 7β-[2-(5-Amino-1,2,4-thiadiazol-3-yl)2-(Z)-methoxyiminoacetamido]-3-(3-oxobutyryloxymethyl)-3-cephem-4-carboxylic acid. In 240 ml of dichloromethane is suspended 9.06 g of 7β-amino-3-(3-oxobutyryloxymethyl)-3-cephem-4-carboxylic acid. To the suspension is added 28.9 g of bistrimethylsilylacetamide and the mixture is stirred at room temperature until complete dissolution and cooled in an ice-water bath. To this solution, 2-(5-amino-1,2,4-thiadiazol-3-yl)-2(Z)-methoxyiminoacetyl chloride hydrochloride prepared from 5.83 g of 2-(5-amino-1,2,4-thiadiazol-3-yl)-2(Z)-methoxyiminoacetic acid and 6.02 g of phosphorous pentachloride in 90 ml of dichloromethane is added and the mixture is stirred for a while. The whole mixture is stirred with ice-cooling for 60 minutes. The dichloromethane is evaporated off and the residue is dissolved in methyl ethyl ketone. The solution is washed with water and dried. The solvent is then evaporated off and diethyl ether is added to the residue to give a fine precipitate, which is collected by filtration, giving 11.8 (82 % yield) g of the title compound. 3300, 3000, 1770, 1710, 1620, 1520, 1400, 1260, 1150, 1040. NMR spectrum (d₆-DMSO) : 2.19(3H,s), 3.40 and 3.65(2H,ABq, J=18Hz), 3.63(2H,s), 3.95(3H,s), 4.78 and 5.09(2H,ABq, J=14Hz), 5.14(1H,d,J=4.8Hz), 5.84(1H,d,d,J=8Hz and 4.8Hz), 8.11(2H,br.), 9.59(1H,d,J=8Hz). Example 1 7β-[2-(5-Amino-1,2,4-thiadiazol-3-yl)2-(Z)-ethoxyiminoacetamido]-3-[(6-cyanoimidazo[1,2-a]pyridinium-1-yl)methyl]-3-cephem-4-carboxylate In 30 ml of a 1:1 mixture of acetonitrile and water are dissolved 2.3 g of 7β-[2-(5-amino-1,2,4-thiadiazol-3-yl)-2(Z)-ethoxyiminoacetamido]-3-(3-oxobutyryloxymethyl)-3-cephem-4-carboxylic acid, 1.79 g of 6-cyanoimidazo[1,2-a]pyridine and 2.2 g of potassium iodide, and the mixture is stirred at 60-70°C for 1.5 hours. The solvent is then evaporated off under reduced pressure and the residue is solidified by addition of 100 ml of acetonitrile. The resulting powder is collected by filtration and then subjected to silica gel column chromatography. The acetonitrile-water (7:3)-eluted fraction is concentrated under reduced pressure and the residue is lyophilized. A solid obtained is dissolved in 5 ml of water and chromatographed on a column of MCI GEL CHP20P® (150-300 meshes; Mitsubishi Chemical Industries, Ltd., Japan) with water-ethanol. The water-ethanol(85:15)-eluated fraction is concentrated under reduced pressure and the residue lyophilized to give 0.27 g of the above-identified compound. Elemental analysis for C₂₂H₁₉N₉O₅S₂ . 4H₂O: Calcd. (%): C, 42.24; H, 4.35; N, 20.15. Found (%): C, 42.12; H, 3.90; N, 19.97. 2250, 1760, 1620, 1525. NMR spectrum (d₆-DMSO) δ : 1.19(3H,t,J=7Hz), 2.98 and 3.44 (2H,ABq,J=18Hz), 4.12(2H,q,J=7Hz), 5.00(1H,d,J=5Hz), 5.1-5.6(2H,m), 5.66(1H,d.d,J=5Hz and 8Hz), 8.10(2H, br.s), 8.2-9.0(4H,m), 9.42(1H,d,J=8Hz), 9.76(1H,br.s). Example 2 7β-[2-(5-Amino-1,2,4-thiadiazol-3-yl)-2(Z)-methoxyiminoacetamido]-3-[(imidazo[1,2-a]pyridinium-1-yl)methyl]-3-cephem-4-carboxylate i) Three grams of 7β[2-(5-tert-butoxycarbonylamino-1,2,4-thiadiazol-3-yl)-2(Z)-methoxyiminoacetamido]-3-(3-oxobutyryloxymethyl)-3-cephem-4-carboxylic acid, 3 g of potassium iodide and 3 g of imidazo[1,2-a]pyridine, are reacted as in Example 1. The reaction mixture is then washed with ethyl acetate, and the aqueous layer is separated and subjected to XAD-2® column chromatography using water as eluent. The reaction product eluted is subjected to silica gel column chromatography (silica gel: 40 g; eluent: acetone-water (6:4)) to give 290 mg of the above-identified compound. Elemental Analysis for C₂₀H₁₈N₈O₅S₂ . 4H₂O: Cald. (%): C, 40.95; H, 4.47; N, 19.10. Found (%): C, 41.15; H, 4.23; N, 18.54. 1770, 1620, 1530, 1390, 1045, 770. NMR spectrum (d₆-DMSO) δ : 2.96 and 3.42(2H,ABq,J=18Hz), 3.86 (3H,s), 4.98(1H,d,J=4.8Hz); 5.26 and 5.48 (2H,ABq, J=14Hz), 5.62(1H,d.d,J=8Hz and 4.8Hz), 7.40-7.60(1H,t), 7.86-8.20(3H,m), 8.34-8.76(3H,m), 8.86-9.00(1H,d), 9.43(1H,d,J=8Hz). Further, another reaction product eluted from the XAD-2® column chromatography using 50 % ethanol as eluent is again subjected to silica gel column chromatography (silica gel: 40 g; eluent: acetone-water (6:4)) to give 240 mg of 7β-[2-(5-tert-butoxycarbonylamino-1,2,4-thiadiazol-3-yl)-2(Z)-methoxyiminoacetamido]-3-[(imidazo[1,2-a]-pyridinium-1-yl)methyl]-3-cephem-4-carboxylate. 1775, 1620, 1530, 1380, 1160, 1045, 770. NMR spectrum (D₂O) δ : 1.50(9H,s), 3.15 and 3.55(2H,ABq, J=18Hz), 4.08(3H,s), 5.23(1H,d,J=4.8Hz), 5.32(2H,s), 5.86(1H,d.J=4.8Hz), 7.09-8.20(7H,m), 8.66(1H,d,J=8Hz). ii) 7β-[2-(5-tert-Butoxycarbonylamino-1,2,4-thiadiazol- 3-yl)-2(Z)-methoxyiminoacetamido]-3-[(imidazo[1,2-a]pyridinium-1-yl)methyl]-3-cephem-4-carboxylate (240 mg) obtained in the above procedure i) is treated with 2 ml of trifluoroacetic acid under ice-cooling. Then, the cooling bath is removed and the reaction mixture is stirred at room temperature for 40 minutes, followed by the addition of ethyl acetate. The mixture is evaporated to dryness under reduced pressure. The residue is dissolved in water, and the solution is neutralized with sodium hydrogen carbonate under ice-cooling and then subjected to XAD-2 column chromatography using 20 % C₂H₅OH as the eluent. The eluted fraction is further subjected to silica gel column chromatography (silica gel: 40 g; eluent: acetone-water (6:4)). Fractions containing the desired product is concentrated and lyophilized to give 310 mg of the above-identified compound. Example 3 7β-[2-(5-Amino-1,2,4-thiadiazol-3-yl)-2(Z)-ethoxyiminoacetamido]-3-[(imidazo[1,2-a]pyridinium-1-yl)methyl]-3-cephem-4-carboxylate 7β-[2-(5-Amino-1,2,4-thiadiazol-3-yl)-2(Z)-ethoxyiminoacetamido]-3-(3-oxobutyryloxymethyl)-3-cephem-4-carboxylic acid and imidazo[1,2-a]pyridine, are reacted in a manner as in Example 1 to give the above-identified compound. Elemental analysis for C₂₁H₂₀N₈O₅S₂ . 4H₂O: Calcd. (%): C, 42.00; H, 4.70; N, 18.66. Found (%): C, 42.25; H, 4.25; H, 18.44. 1770, 1610, 1530, 1390, 1360, 1040, 765. NMR spectrum (d₆-DMSO) δ : 1.20(3H,t,J=7Hz), 3.02 and 3.44 (2H,ABq,J=18Hz), 4.12(2H,q,J=7Hz), 5.01(1H,d,J=4.8Hz), 5.42(2H,br.s), 5.66(1H,d.d,J=8Hz and 4.8Hz), 7.50(t, J=7Hz), 8.00(t,J=7Hz), 8.40-7.00(m) and 8.98(d,J=7Hz), (total 6H), 9.42(1H,d,J=8Hz), 8.16(2H,s). Example 4 7β-[2-(5-Amino-1,2,4-thiadiazol-3-yl)-2(Z)-ethoxyiminoacetamido]-3-[(6-chloroimidazo[1,2-a]pyridinium-1-yl)methyl] -3-cephem-4-carboxylate 7β-[2-(5-Amino-1,2,4-thiadiazol-3-yl)-2(Z)-ethoxyiminoacetamido]-3-(3-oxobutyryloxymethyl)-3-cephem-4-carboxylic acid and 6-chloroimidazo[1,2-a]pyridine are reacted in a manner as in Example 1 to give the above-identified compound. Elemental analysis for C₂₁H₁₉ClN₈O₅S₂ . 3H₂O: Calcd. (%): C, 40.88; H, 4.08; N, 18.16. Found (%): C, 40.85; H, 3.97; N, 18.01. 3300, 3150, 1780, 1680, 1620, 1520, 1390, 1040 NMR spectrum (d₆-DMSO) δ : 1.11(3H,t,J=7Hz), 2.99 and 3.44 (2H,ABq;J=18Hz), 4.13(2H,q,J=7Hz), 5.00(1H,d,J=4.8Hz), 5.27 and 5.49(2H,ABq,J=14Hz), 5.66(1H,d.d,J=8Hz and 4.8Hz), 8.00-8.86(m) and 9.30(s) (total 5H), 9.42(1H, d,J=8Hz). Example 5 7β-[2-(5-Amino-1,2,4-thiadiazol-3-yl)-2(Z)-ethoxyiminoacetamido]-3-[3-(dimethylaminomethyl)imidazo[1,2-a]pyridinium-1-yl)methyl]-3-cephem-4-carboxylate 7β-[2-(5-Amino-1,2,4-thiadiazol-3-yl)-2(Z)-ethoxyiminoacetamido]-3-(3-oxobutyryloxymethyl)3-cephem-4-carboxylic acid and 3-(dimethylaminomethyl)imidazo[1,2-a]pyridine are reacted in a manner as in Example 1 to give the above-identified compound. Elemental analysis for C₂₄H₂₇N₉O₅S₂ . 3H₂O: Calcd. (%): C, 45.06; H, 5.20; N, 19.71. Found (%): C, 45.18; H, 4.68; N, 19,57. 1770, 1660, 1615, 1530. NMR spectrum (d₆-DMSO) δ : 1.26(3H,t,J=7Hz), 2.90(3H,s), 2.98 (3H,s) , 4.17(2H,q,J=7Hz), 5.06(2H,br.s), 5.19(1H,d, J=4.5Hz), 5.68(1H,d.d,J=4.5Hz and 8Hz), 6.96-7.56(2H, m), 7.54-7.76(1H,m), 7.84-8.00(1H,m), 8.10(2H,br.s), 8.76-9.00(1H,m), 9.48(1H,d,J=8Hz). Example 6 7β-[2-(5-Amino-1,2,4-thiadiazol-3-yl)-2(Z)-methoxyiminoacetamido]-3-[(imidazo[1,2-b]pyridazinium-1-yl)methyl]-3-cephem-4-carboxylate hydrochloride. To a solution of 7β-[2-(5-amino-1,2,4-thiadiazol-3-yl)-2(Z)-methoxyiminoacetamido]-3-[(imidazo[1,2-b]pyridazinium-1-yl)methyl]-3-cephem-4-carboxylate (130 mg) in 0.4 ml of water, 200 µl of 1N hydrochloric acid is added. To this, 20 ml of acetone is added and the mixture is stirred for 5 minutes. The precipitate separated is collected by filtration, washed with small amount of acetone and dried to give the title compound. 1780, 1675, 1620, 1520, 1450, 1380, 1220. Example 7 7β-[2-(5-Amino-1,2,4-thiadiazol-3-yl)-2(Z)-cyanomethyloxyiminoacetamido]-3-[(imidazo[1,2-a]pyridinium-1-yl)methyl]-3-cephem-4-carboxylate Two grams of 7β-[2-(5-amino-1,2,4-thiadiazol-3-yl)-2(Z)-cyanomethoxyiminoacetamido]-3-(3-oxobutyryloxymethyl)-3-cephem-4-carboxylic acid obtained in Reference Example 3, 2 g of imidazo[1,2-a]pyridine and 2 g of sodium iodide are mixed in a mixture of 20 ml each of acetonitrile and water and the mixture is heated in an oil bath kept at 75°C for 60 minutes with stirring and then allowed to cool. To the reaction mixture, 50 ml of ethyl acetate is added and, after shaking, the aqueous layer is separated and concentrated. The residue is then placed on a XAD-2 column and eluted first with water, then with 20 % ethanol in water. Fractions containing the objective compound are concentrated and filtered to remove some insoluble materials. The filtrate is lyophilized and the product obtained is dissolved in small amount of water and subjected to chromatography on a column of silica gel. The column is washed with acetone and then the desired product is eluted with acetone:water = 7:3. Fractions containing the objective compound are concentrated and the residue is lyophilized to give the above-identified compound. 3100, 1760, 1605, 1520, 1380, 1040, 1010, 760. NMR spectrum (D₂O) δ : 3.16 and 3.53(2H,ABq,J=18Hz), 5.15(1H, d,J=4.8Hz), 5.31(2H,br.s), 5.82(1H,d,J=4.8Hz), 7.40-7.80, 7.90-8.30 and 8.60-8.80(6H,m). Example 8 7β-[2-(5-Amino-1,2,4-thiadiazol-3-yl)-2(Z)-ethoxyiminoacetamido]-3-[(3-cyanoimidazo[1,2-a]pyridinium-1-yl)methyl]-3-cephem-4-carboxylate 7β-[2-(5-Amino-1,2,4-thiadiazol-3-yl)-2(Z)-ethoxyiminoacetamido]-3-(3-oxobutyryloxymethyl)-3-cephem-4-carboxylic acid and 3-cyanoimidazo[1,2-a]pyridine are reacted in a manner as in Example 1 to give the above-identified compound. Elemental analysis for C₂₂H₁₉N₉O₅S₂ . 3H₂O: Calcd. (%): C, 43.49; H, 4.15; N, 20.45. Found (%): C, 43.58; H, 3.59; N, 20.38. 2245, 1770, 1680, 1640, 1610, 1510. NMR spectrum (d₆-DMSO) δ : 1.20(3H,t,J=7Hz), 3.01(1H,ABqx1/2, J=18Hz), 4.12(2H,d,J=7Hz), 4.98(1H,d,J=4.5Hz), 5.33 and 5.58(2H,ABq,J=14Hz), 5.65(1H,d.d,J=4.5Hz and 8Hz), 7.64-7.88(1H,m), 8.04(2H,br.s), 8.00-8.48(1H,m), 8.92-9.12(2H,m), 9.42(1H,d,J=8Hz), 9.47(1H,s). Example 9 7β-[2-(5-Amino-1,2,4-thiadiazol-3-yl)-2(Z)-cyanomethoxyiminoacetamido]-3-[(6-cyanoimidazo[1,2-a]pyridinium-1-yl)methyl]-3-cephem-4-carboxylate The compound obtained in Reference Example 3 and 6-cyanoimidazo[1,2-a]pyridine are reacted in a manner as in Example 1 to give the above-identified compound. Elemental analysis for C₂₃H₁₇N₉O₅S₂ . 4.5H₂O: Calcd. (%): C, 42.85; H, 4.07; N, 19.56. Found (%): C, 42.68; H, 4.01; N, 19.51. 3400, 2250, 1760, 1670, 1650, 1610, 1530. NMR spectrum (d₆-DMSO) δ : 2.96 and 3.46(2H,ABq,J=16Hz), 5.01 (1H,d,J=5Hz), 5.02(2H,s), 5.27 and 5.53(2H,ABq,J=15Hz), 5.64(1H,d.d,J=5Hz and 8Hz), 8.2-9.0(4H,m), 8.22(2H, br.s), 9.66(1H,d,J=8Hz), 9.77(1H,br.s). Example 10 7β-[2-(5-Amino-1,2,4-thiadiazol-3-yl)-2(Z)-methoxyiminoacetamido]-3-[(6-cyanoimidazo[1,2-a]pyridinium-1-yl)methyl]-3-cephem-4-carboxylate The compound obtained in Reference Example 1 and 6-cyanoimidazo[1,2-a]pyridine are reacted in a manner as in Example 2 to give the above-identified compound. Elemental analysis for C₂₁H₁₇N₉O₅S₂ . 3H₂O: Calcd. (%): C, 42.49; H, 3.91; N, 21.24. Found (%): C, 42.56; H, 3.67; N, 21.01. 3450, 2250, 1760, 1600, 1520. NMR (d₆-DMSO) δ : 2.98 and 3.46(2H,ABq,J=16Hz), 3.86(3H,s), 5.00(1H,d,J=5Hz), 5.28 and 5.54(2H,ABq,J=15Hz), 5.64 (1H,d.d, J=5Hz and 8Hz), 8.11(2H,br.s), 8.2-9.0(5H,m), 9.44(1H,d,J=8Hz), 9,78(1H,br.s). Example 11 7β-[2-(5-Amino-1,2,4-thiadiazol-3-yl)-2(Z)-carboxymethoxyiminoacetamido]-3-[(6-cyanoimidazo[1,2-a]-pyridinium-1-yl)methyl]-3-cephem-4-carboxylate monosodium salt One gram of 7β-[2-(5-amino-1,2,4-thiadiazol-3-yl)-2(Z)-carboxymethoxyiminoacetamido]-3-(3-oxobutyryloxymethyl)-3-cephem-4-carboxylic acid, obtained as in Example 12 (iii), 1 g of 6-cyanoimidazo[1,2-a]pyridine and 1 g of sodium iodide are added in a mixture of 15 ml of acetonitrile and 15 ml of water and the mixture is heated in an oil bath kept at 70-75°C for 1.5 hours with stirring. The reaction mixture is shaken with ethyl acetate and the aqueous layer is separated, concentrated under reduced pressure and chromatographed on a silica gel column with acetone and then acetone:water = 7:3. Fractions containing the objective compound are concentrated and the residue is lyophilized to give the above-identified compound. Elemental analysis for C₂₂H₁₆N₉O₇S₂Na . 5H₂O Calcd. (%): C, 37.99; H, 3.77; N, 18.12. Found (%): C, 38.18; H, 3.33; N, 17.15. 2240, 1760, 1600, 1520, 1400, 1360, 1045. NMR spectrum (D₂O) δ : 3.16 and 3.59(2H,ABq,J=18Hz), 5.24 (1H,d,J=4.8Hz), 5.38(2H,br.s), 5.86(1H,d,J=4.8Hz), 8.2-9.0(4H,m), 9.8(1H,br.s). Example 12 7β-[2-(5-Amino-1,2,4-thiadiazol-3-yl)-2(Z)-carboxymethoxyiminoacetamido]-3-[(imidazo[1,2-a]pyridinium-1-yl)methyl]-3-cephem-4-carboxylate i) To a solution of 2-(5-tert-butoxycarbonylamino-1,2,4-thiadiazol-3-yl)-2-oxoacetic acid in ethanol (100ml), prepared from 13 g of 2-(5-amino-1,2,4-thiadiazol-3-yl)acetic acid and 10.7 g of selenium dioxide in a manner as in Reference Example 3, is added, under ice-cooling, 6.2 g of O-tert-butoxycarbonylmethylhydroxylamine (prepared from 14 g of N-tert-butoxycarbonylmethoxyphthalimide and 2.3 g of methylhydrazine) and the mixture is stirred at room temperature for 4 hours. Ethanol is then evaporated off and the residue is shaken with ethyl acetate and water. The organic layer is separated and extracted with an aqueous sodium bicarbonate solution. The aqueous extract is made acid with 1N-HCl and extracted with ethyl acetate. The extract is dried over anhydrous magnesium sulfate. The solvent is then evaporated off and the residue is crystallized from hexane to give, after filtration and drying, 11 g of 2-(5-tert-butoxycarbonylamino-1,2,4-thiadiazol-3-yl)-2(Z)-(tert-butoxycarbonylmethoxyimino)acetic acid. mp 128°C (decomposition) NMR spectrum (CDCl₃) : 1.43(9H,s), 1.55(9H,s), 4.73(2H,s). ii) To a solution of 13 g of 2-(tert-butoxycarbonylamino-1,2,4-thiadiazol-3-yl)-2(Z)-(tert-butoxycarbonylmethoxyimino)acetic acid in 100 ml of dichloromethane, 7 g of phosphorous pentachloride is added and the mixture is stirred for 20 minutes under ice-cooling. The reaction mixture is evaporated to dryness and to the residue is added hexane and the solvent is evaporated off again. The residue is dissolved in 5 ml of dichloromethane and the solution is added under ice-cooling to a solution prepared by allowing 10 g of 7β-amino-3-(3-oxobutyryloxymethyl)-3-cephem-4-carboxylic acid and 16 g of N,O-bistrimethylsilylacetamide to react in 200 ml of dichloromethane at room temperature for one hour. The mixture is stirred at the same temperature for one hour and the solvent is then evaporated under reduced pressure. The residue is dissolved in 300 ml of ethyl acetate and the solution is washed with water and then dried over anhydrous magnesium sulfate. Then, the solvent is evaporated off and the residue is triturated with hexane. Insoluble substance is collected by filtration to give 23 g of 7β[2-(5-tert-butoxycarbonylamino-1,2,4-thiadiazol-3-yl)-2(Z)-(tert-butoxycarbonylmethoxyimino)acetamido]-3-(3-oxobutyryloxymethyl)3-cephem-4-carboxylic acid. 3250, 2960, 1780, 1715, 1540, 1370, 1205, 1150, 1060. NMR spectrum (d₆-DMSO) δ : 1.43(9H,s), 1.50(9H,s), 2.18(3H,s), 3.41 and 3.65(2H,ABq,J=18Hz), 3.62(2H,s), 4.66(2H,s), 4.78 and 5.06(2H,ABq,J=12Hz), 5.15(1H,d,J=4.8Hz), 5.86 (1H,d.d,J=4.8Hz and 8Hz), 9.56(1H,d,J=8Hz). iii) The whole amount of the compound obtained in ii) is added to 50 ml of trifluoroacetic acid under ice-cooling. Then, the cooling-bath is removed and the reaction mixture is stirred at room temperature for 1.5 hours. After being diluted with ethyl acetate, the reaction mixture is evaporated off to dryness and the residue is triturated with ethyl acetate. Insoluble substance is collected by filtration to give 12 g of 7β[2-(5-amino-1,2,4-thiadiazol-3-yl)-2(Z)-carboxymethoxyiminoacetamido]-3-(3-oxobutyryloxymethyl)-3-cephem-4-carboxylic acid. From the filtrate, after evaporation to dryness, addition of diethyl ether to the residue and filtration of insoluble material, 5 g of the same objective compound is recovered. 1760, 1720, 1630, 1520, 1400, 1310, 1180, 1145. NMR spectrum (D₆-DMSO) δ : 2.20(3H,s), 3.41 and 3.65(2H,ABq, J=18Hz), 3.63(2H,s), 4.65(2H,s), 4.78 and 5.07(2H,ABq, J=12Hz), 5.15(1H,d,J=4.8Hz), 5.85(1H,d.d,J=4.8Hz and 8Hz), 8.10(2H,br.), 9.48(1H,d,J=8Hz). iv) One gram of 7β-[2-(5-amino-1,2,4-thiadiazol-3-yl)-2(Z)-carboxymethoxyiminoacetamido]-3-(3-oxobutyryloxymethyl)-3-cephem-4-carboxylic acid, 1 g of imidazo[1,2-a]pyridine and 1 g of sodium iodide are added to a mixture of 10 ml of acetonitrile and 10 ml of water and heated in an oil bath kept at 70-75°C for 1.5 hours. The reaction mixture is worked up as in Example 1 to give the above-identified compound. Elemental analysis for C₂₁H₁₇N₈O₇S₂Na . 5H₂O: Calcd. (%): C, 42.79; H, 3.08; N, 19.01. Found (%): C, 42.88; H, 3.64; N, 17.55. 1760, 1600, 1520, 1400, 1305, 1050. NMR spectrum (D₂O) δ : 3.16 and 3.53(2H,ABq,J=18Hz), 5.22 (1H,d,J=4.8Hz), 5.32(2H,br.s), 5.86(1H,d,J=4.8Hz), 7.40-8.80(6H,m). Example 13 7β-[2-(5-Amino-1,2,4-thiadiazol-3-yl)-2(Z)-methoxyiminoacetamido]-3-[(imidazo[1,2-b]pyridazinium-1-yl)methyl]-3-cephem-4-carboxylate 7β-[2-(5-Amino-1,2,4-thiadiazol-3-yl)-2(Z)-methoxyiminoacetamido]-3-(3-oxobutyryloxymethyl)-3-cephem-4-carboxylic acid (1.1 g), imidazo[1,2-b]pyridazine (1.0 g) and potassium iodide (1.1 g) are dissolved in 30 ml of 50 % aqueous acetonitrile and the mixture is heated for 2 hours at 60-70°C. After cooling, the reaction mixture is chromatographed on a column of silica gel with acetone and then with aqueous acetone, successively. Fractions containing the objective compound are combined and concentrated under reduced pressure. The residue is then chromatographed on a column of MCI gel CHP20P® resin (Mitsubishi Kasei, Japan) with water and then with aqueous alcohol. Fractions containing the object compound are combined and concentrated and the residue is lyophilized to give the title compound. Elemental analysis for C₁₉H₁₇N₉O₅S₂ . 3H₂O Calcd. (%): C, 40.07; H, 4.07; N, 22.13. Found (%): C, 39.75; H, 3.51; N, 21.89. 1765, 1660, 1610, 1520. NMR spectrum (d₆-DMSO) δ : 3.03 and 3.44(2H,ABq,J=18Hz), 3.86(3H,s), 4.99(1H,d,J=4.5Hz), 5.27 and 5.51(2H,ABq, J=14Hz), 5.63(1H,d.d,J=4.5Hz and 8Hz), 7.8-8.32(1H,m), 8.12(2H,br.s), 8.76(2H,s), 9.04(1H,d,J=4Hz), 9.31(1H, d,J=9Hz), 9.44(1H,d,J=8Hz). Example 14 7β-[2-(5-Amino-1,2,4-thiadiazol-3-yl)-2(Z)-ethoxyiminoacetamido]-3-[(imidazo[1,2-b]pyridazinium-1-yl)methyl]-3-cephem-4-carboxylate 7β-[2-(5-Amino-1,2,4-thiadiazol-3-yl)-2(Z)-ethoxyiminoacetamido]-3-(oxobutyryloxymethyl)-3-cephem-4-carboxylic acid is made to react with imidazo[1,2-b]pyridazine by the procedure of Example 1 to give the title compound. Elemental analysis for C₂₀H₁₉N₉O₅S₂ . 4H₂O Calcd. (%): C, 39.93; H, 4.52; N, 20.95. Found (%): C, 40.35; H, 4.68; N, 20.68. 1770, 1670, 1610, 1520. NMR spectrum (d₆-DMSO) δ : 1.20(3H,t,J=7Hz), 3.03 and 3.44(2H, ABq,J=18Hz), 4.13(2H,q,J=7Hz), 4.99(1H,d,J=4.5Hz), 5.28 and 5.52(2H,ABq,J=14Hz), 5.65(1H,d.d,J=4.5Hz and 8Hz), 7.8-8.2(1H,m), 8.75(2H,s), 9.05(1H,d,J=4Hz), 9.28(1H, s), 9.43(1H,d,J=8Hz). Example 15 7β-[2-(5-Amino-1,2,4-thiadiazol-3-yl)-2(Z)-methoxyiminoacetamido]-3-[(8-methylimidazo[1,2-b]pyridazinium-1-yl)methyl]-3-cephem-4-carboxylate By the procedure of Example 1, 7β-[2-(5-amino-1,2,4-thiadiazol-3-yl)-2(Z)-methoxyiminoacetamido]-3-(3-oxobutyryloxymethyl)-3-cephem-4-carboxylic acid is reacted with 8-methylimidazo[1,2-b]pyridazine to give the title compound. Elemental analysis for C₂₀H₁₉N₉O₅S₂ . 4H₂O Calcd. (%): C, 39.34; H, 4.62; N, 20.64. Found (%): C, 39.48; H, 4.92; N, 20.74. 1765; 1670; 1610, 1520. NMR spectrum (d₆-DMSO) δ : 2.17(3H,s), 3.90(3H,s), 3.06 and 3.39(2H,ABq,J=18Hz), 5.09(1H,d,J=4.5Hz), 5.50(2H,br,s), 5.70(1H,d.d,J=4.5Hz and 8Hz), 7.68(1H,d,J=5Hz), 7.97 (2H,br.s), 8.32-8.52(1H,m), 8.56-8.66(1H,m), 8.84(1H, d,J=5Hz), 9.47(1H,d,J=8Hz). Example 16 7β-[2-(5-Amino-1,2,4-thiadiazol-3-yl)-2(Z)-ethoxyiminoacetamido]-3-[(5-methylimidazo[1,5-a]pyridinium-2-yl)methyl]-3-cephem-4-carboxylate By the procedure of Example 1, 7β-[2-(5-amino-1,2,4-thiadiazol-3-yl)-2(Z)-ethoxyiminoacetamido]-3-(3-oxobutyryloxymethyl)-3-cephem-4-carboxylic acid is reacted with 5-methylimidazo[1,5-a]pyridine to give the title compound. Elemental analysis for C₂₂H₂₂N₈O₅S₂ . 2H₂O Calcd. (%): C, 45,67; H, 4.53; N, 19.37. Found (%): C, 45,31; H, 5.00; N, 19.21. 1760, 1660, 1610, 1510, 1390, 1350. NMR spectrum (d₆-DMsO) δ : 1.20(3H,t,J=7Hz), 2.66(3H,s), 3.17 (2Hx1/2,ABq,J=18Hz), 4.12(2H,q,J=17Hz), 5.03(1H,d, J=5Hz), 5.06 and 5.54(2H,ABq,J=14Hz), 5.67(1H,d.d,J=5Hz and 8Hz), 6.9-7.4(2H,m), 7.79(1H,d,J=8Hz), 8.09(1H, br.s), 8.63(1H,s), 9.39(1H,d,J=8Hz), 9.93(1H,s). Example 17 7β-[2-(5-Amino-1,2,4-thiadiazol-3-yl)-2(Z)-methoxyiminoacetamido]-3-[(6-methylimidazo[1,2-b]pyridazinium-1-yl)methyl]-3-cephem-4-carboxylate By the procedure of Example 1 7β[2-(5-amino-1,2,4-thiadiazol-3-yl)-2(Z)-methoxyiminoacetamido]-3-(3-oxobutyryloxymethyl)-3-cephem-4-carboxylic acid is reacted with 6-methylimidazo[1,2-b]pyridazine to give the title compound. Elemental analysis for C₂₀H₁₉N₉O₅S₂ . 5H₂O Calcd. (%): C, 38.77; H, 4.72; N, 20.34. Found (%): C, 38.94; H, 4.69; N, 20.32. 1765, 1660, 1605, 1520. NMR spectrum (d₆-DMSO) δ : 2.99 and 3.43(2H,ABq,J=18Hz), 2.67 (3H,s), 3.86(3H,s), 4.97(1H,d,J=4.5Hz), 5.24 and 5.40 (2H,ABq,J=14Hz), 5.61(1H,d.d,J=4.5Hz and 8Hz), 7.86(1H, d,J=9Hz), 8.10(2H,br.s), 8.58-8.76(2H,m), 9.20(1H,d, J=9Hz), 9.43(1H,d,J=8Hz). By the procedure of Example 1, compounds of the following Examples 18-24 can be prepared by reacting 7β-[2-(5-amino-1,2,4-thiadiazol-3-yl)-2(Z)-methoxyiminoacetamido]-3-(3-oxobutyryloxymethyl)-3-cephem-4-carboxylic acid with various imidazo[1,2-b]pyridazines. Example 18 7β-[2-(5-Amino-1,2,4-thiadiazol-3-yl)-2(Z)-methoxyiminoacetamido]-3-[(6-ethoxyimidazo[1,2-b]pyridazinium-1-yl)methyl]-3-cephem-4-carboxylate Elemental analysis for C₂₁H₂₁N₉O₆S₂ . 3H₂O Calcd. (%): C, 41.11; H, 4.43; N, 20.54. Found (%): C, 40.95; H, 4.56; N, 20.32. 1770, 1670, 1600, 1500. NMR spectrum (d₆-DMSO) δ : 1.44(3H,t,J=7Hz), 2.98 and 3.42 (2H,ABq,J=18Hz), 3.87(3H,s), 4.46(2H,q,J=7Hz), 4.98 (1H,d,J=4.5Hz), 5.20 and 5.50(2H,ABq,J=14Hz), 5.60(1H, d.d,J=4.5Hz and 8Hz), 7.57(2H,d,J=14Hz), 8.04(2H,br.s), 8.46(1H,d,J=2Hz), 8.64(1H,d,J=2Hz), 9.24(1H,d,J=10Hz), 9.40(1H,d,J=8Hz). Example 19 7β-[2-(5-Amino-1,2,4-thiadiazol-3-yl)-2(Z)-methoxyiminoacetamido]-3-[(6-methylthioimidazo[1,2-b]pyridazinium-1-yl)methyl]-3-cephem-4-carboxylate Elemental analysis for C₂₀H₁₉N₉O₅S₃ . 7/2H₂O Calcd. (%): C, 38.45; H, 4.20; N, 20.18. Found (%): C, 38.40; H, 4.25; H, 20.11. 1770, 1670, 1600, 1520. NMR spectrum (d₆-DMSO) δ : 2.66(3H,s), 3.01(2Hx1/2,ABqx1/2, J=18Hz), 3.86(3H,s), 4.98(1H,d,J=4.5Hz), 5.22 and 5.50 (2H,d,J=14Hz), 5.63(1H,d.d,J=4.5Hz and 8Hz), 7.91(1H,d, J=10Hz), 8.10(2H,br.s), 8.54-8.74(2H,m), 9.22(1H,d, J=10Hz), 9.44(1H,d,J=8Hz). Example 20 7β-[2-(5-Amino-1,2,4-thiadiazol-3-yl)-2(Z)-methoxyiminoacetamido]-3-[(6-chloroimidazo[1,2-b]pyridazinium-1-yl)methyl]-3-cephem-4-carboxylate Elemental analysis for C₁₉H₁₆ClN₉O₅S₂ . 4H₂O Calcd. (%): C, 36.69; H, 3.89; N, 20.27. Found (%): C, 36.80; H, 3.12; N, 20.09. 1775, 1670, 1610, 1520. NMR spectrum (d₆-DMSO) δ : 2.98 and 3.42(2H,ABq,J=18Hz), 3.86 (3H,s), 4.98(1H,d,J=4.5Hz), 5.24 and 5.55(2H,ABq, J=14Hz), 5.59(1H,d.d,J=4.5Hz and 8Hz), 8.09(2H,br.s), 8.17(1H,d,J=9Hz), 8.73-8.90(2H,m), 9.42(1H,d,J=8Hz), 9.48(1H,d,J=9Hz). Example 21 7β-[2-(5-Amino-1,2,4-thiadiazol-3-yl)-2(Z)-methoxyiminoacetamido]-3-[(6-methoxyimidazo[1,2-b]pyridazinium-1-yl]-3-cephem-4-carboxylate Elemental analysis for C₂₀H₁₉N₉O₆S₂ . 9/2H₂O Calcd. (%): C, 38.34; H, 4.50; N, 20.12. Found (%): C, 38.39; H, 4.54; N, 20.02. 1770, 1670, 1610, 1510. NMR spectrum (d₆-DMSO) δ : 2.98 and 3.43(2H,ABq,J=18Hz), 3.86 (3H,s), 4.06(3H,s), 4.97(1H,d,J=4.5Hz), 5.20 and 5.50 (2H,ABq,J=14Hz), 5.62(1H,d.d,J=4.5Hz and 8Hz), 7.62(1H, d,J=9Hz), 8.04(2H,br.s), 8.38-8.68(2H,m), 9.22(1H,d, J=9Hz), 9.42(1H,d,J=8Hz). Example 22 7β-[2-(5-Amino-1,2,4-thiadiazol-3-yl)-2(Z)-methoxyiminoacetamido]-3-[(6-methylimidazo[1,2-b]pyridazinium-1-yl)methyl]-3-cephem-4-carboxylate Elemental analysis for C₂₀H₁₉N₉O₅S₂ . 5H₂O Calcd. (%): C, 38.77; H, 4.72; N, 20.34. Found (%): C, 38.94; H, 4.69; N, 20.32. 1765, 1660, 1605, 1520. NMR spectrum (d₆-DMSO) δ : 2.99 and 3.43(2H,ABq,J=18Hz), 2.67 (3H,s), 3.86(3H,s), 4.97(1H,d,J=4.5Hz), 5.24 and 5.40 (2H,ABq,J=14Hz), 5.61(1H,d.d,J=4.5Hz and 8Hz), 7.86(1H, d,J=9Hz), 8.10(2H,br.s), 8.58-8.76(2H,m), 9.20(1H,d, J=9Hz), 9.43(1H,d,J=8Hz). Example 23 7β-[2-(5-Amino-1,2,4-thiadiazol-3-yl)-2(Z)-methoxyiminoacetamido]-3-[(6-dimethylaminoimidazo[1,2-b]pyridazinium-1-yl)methyl]-3-cephem-4-carboxylate Elemental analysis for C₂₁H₂₂N₁₀O₅S₂ . 4H₂O Calcd. (%): C, 39.99; H, 4.79; N, 22.21. Found (%): C, 40.26; H, 3.90; N, 22,07. 1775, 1670, 1610, 1590, 1510. NMR spectrum (d₆-DMSO) δ : 3.04(2H,br.s), 3.14(6H,s), 3.86 (3H,s), 4.96(1H,d,J=4.5Hz), 5.15. and 5.43(2H,ABq, J=14Hz), 5.57(1H,d.d,J=4.5Hz and 8Hz), 7.68(1H,d, J=10Hz), 8.07(2H,br.s), 8.24(1H,br.s), 8.39(1H,br.s), 8.96(1H,d,J=10Hz), 9.40(1H,d,J=8Hz). Example 24 7β[2-(5-Amino-1,2,4-thiadiazol-3-yl)-2(Z)-methoxyiminoacetamido]-3-[(6-fluoroimidazo[1,2-b]pyridazinium-1-yl)methyl]-3-cephem-4-carboxylate Elemental analysis for C₁₉H₁₆N₉O₅S₂F . 4H₂O Calcd. (%): C, 37.69; H, 3.99; N, 20.82. Found (%): C, 38.03; H, 3.89; N, 20.55. 1770, 1670, 1610, 1520. NMR spectrum (d₆-DMSO) δ : 3.00(2Hx1/2,ABqx1/2,J=18Hz), 3.86 (3H,s), 4.98(1H,d,J=4.5Hz), 5.26 and 5.59(2H,ABq, J=14Hz), 5.62(1H,d.d,J=4.5Hz and 8Hz), 7.9-8.24(3H,m), 8.62-8.86(2H,m), 9.41(1H,d,J=8Hz), 9.48-9.74(1H,m). Example 25 7β-[2-(5-Amino-1,2,4-thiadiazol-3-yl-2(Z)-carboxymethoxyiminoacetamido]-3-[(imidazo(1,2-b)pyridazinium-1-yl)methyl]-3-cephem-4-carboxylate . mono-sodium salt By the procedure of Example 1, 7β[(2-(5-amino-1,2,4-thiadiazol-3-yl)-2(Z)-carboxymethoxyiminoacetamido]-3-(3-oxobutyryloxymethyl)-3-cephem-4-carboxylic acid is made to react with imidazo[1,2-b]pyridazine to give the title compound. Elemental analysis for C₂₀H₁₆N₉O₇S₂N₉ . 3/2H₂O Calcd. (%): C, 34.38; H, 4.18; N, 18.04. Found (%): C, 34.48; H, 3.64; N, 17.54. 1770, 1600, 1520. NMR spectrum (d₆-DMSO) δ : 3.52 and 3.72(1H,ABq,J=18Hz), 4.34 (2H,s), 4.98(1H,d,J=4.5Hz), 5.34 and 5.50(2H,ABq, J=14Hz), 5.68(1H,d,J=4.5Hz), 7.90(1H,d.d,J=5Hz and 10Hz), 8.17(1H,d,J=10Hz). Example 26 7β-[2-(5-Amino-1,2,4-thiadiazol-3-yl)-2(Z)-methoxyiminoacetamido]-3-[(6-(2-dimethylaminoethylthio)imidazo[1,2-b]pyridazinium-1-yl)methyl]-3-cephem-4-carboxylate . dihydrochloride 7β-[2-(5-amino-1,2,4-thiadiazol-3-yl)-2(Z)-methoxyiminoacetamido]-3-(3-oxobutyryloxymethyl)-3-cephem-4-carboxylic acid (1.5 g), 6-(2-dimethylaminoethylthio)imidazo[1,2-b]pyridazine (1.5 g) and potassium iodide (1.5 g) are dissolved in a mixture of 5 ml of 1N hydrochloric acid, 5 ml of water and 10 ml of acetonitrile and the solution is heated for 2 hours at 60-70°C with stirring. The acetonitrile is evaporated under reduced pressure and the residue is chromatographed on a column of high porous polymer MCl gel CHP20P® (Mitsubishi Kasei, Japan) with 0.01N hydrochloric acid. Fractions containing the object compound are combined and concentrated under reduced pressure and the residue is lyophilized to give 0.13 g of the title compound. Elemental analysis for C₂₃H₂₄N₁₀O₅S₃ . 2H₂O . 11/2H₂O Calcd. (%): C, 35.03; H, 4.73; N, 17.76. Found (%): C, 35.15; H, 4.46; N, 17.66. 1770, 1675, 1625, 1510. NMR spectrum (d₆-DMSO-D₂O) δ : 2.90(6H,s), 3.3-3.85(6H,m), 4.08(3H,s), 5.18(1H,d,J=4.5Hz), 5.46(2H,br.s), 5.82 (1H,d,J=4.5Hz), 7.97(1H,d,J=10Hz), 8.27(1H,br.s), 8.73(1H,d,J=10Hz), 8.79(1H,br.s). Example 27 7β-[2-(5-Amino-1,2,4-thiadiazol-3-yl)-2(Z)-methoxyiminoacetamido]-3-[(7-methylimidazo(1,2-b)pyridazinium-1-yl)methyl]-3-cephem-4-carboxylate By the procedure of Example 1, 7β-2-(5-amino-1,2,4-thiadiazol-3-yl)-2(Z)-methoxyiminoacetamido)-3-(3-oxobutyryloxymethyl)-3-cephem-4-carboxylic acid is made to react with 7-methylimidazo[1,2-b]pyridazine to give the title compound. Elemental analysis for C₂₀H₁₉N₉O₅S₂ . 5H₂O Calcd. (%): C, 38.77; H, 4.72; N, 20,34. Found (%): C, 38.82; H, 4.75; N, 20.32. 1760, 1665, 1610, 1520. NMR spectrum (d₆-DMSO) δ : 2.56(3H,s), 3.00(2Hx1/2,ABqx1/2, J=18Hz), 3.86(3H,s), 4.99(1H,d,J=4.5Hz), 5.20 and 5.43 (2H,ABq,J=14Hz), 5.62(1H,d.d,J=4.5Hz and 8Hz), 8.09(2H, br.s), 8.58-8.74(2H,m), 8.97(1H,br.s), 9.08(1H,br.s), 9.42(1H,d,J=8Hz). Example 28 7β-[2-(5-Amino-1,2,4-thiadiazol-3-yl)-2(Z)-methoxyiminoacetamido]-3-[(imidazo[1,2-b]pyridazinium-1-yl)methyl]-3-cephem-4-carboxylate (1) 7β-tert-Butoxycarbonylamino-3-(3-oxobutyryloxymethyl)-3-cephem-4-carboxylic acid (4.14 g), imidazo[1,2-b]pyridazine (4.14 g) and sodium iodide (8.28 g) are added to a mixture of 20 ml of water and 20 ml of acetonitrile and the mixture is heated for 2 hours at 70°C with stirring. After being allowed to cool to room temperature, the reaction mixture is subjected to silica gel (100 g) column chromatography. The column is washed with acetone and 95 % acetone-water and then the product is eluted with 75 % acetone-water. Fractions containing the object compound are combined and concentrated and the residue is lyophilized to give 1.14 g of 7β-tert-butoxycarbonylamino-3-[(imidazo[1,2-b]pyridazinium-1--yl)methyl]-3-cephem-4-carboxylate as a powder. 1760, 1710, 1610, 1520, 1385, 1370. NMR spectrum (d₆-DMSO) δ : 1.39(9H,s), 3.08 and 3.48(2H,ABq, J=18Hz), 4.91(1H,d,J=6Hz), 5.1-5.6(3H,m), 7.6-8.2(2H, m), 8.78(2H,br.s), 9.07(1H,d,J=4Hz), 9.31(1H,d,J=10Hz). TLC (Merck, Art 5715; solvent: acetonitrile:water = 4:1), Rf = 0.4. (2) 7β-(tert-Butoxycarbonylamino)-3-[(imidazo[1,2-b]pyridazinium-1-yl)methyl]-3-cephem-4-carboxylate (1.45 g) is dissolved in 20 ml of trifluoroacetic acid and the solution is stirred at room temperature for 30 minutes. The reaction mixture is concentrated under reduced pressure and the residue is treated with 100 ml of ether with stirring. Precipitate separated is collected by filtration and washed with ether to give 1.42 g of 7β-amino-3-(imidazo[1,2-b]pyridazinium-1-yl)methyl-3-cephem-4-carboxylate trifluoroacetate. The yield: 95 %. 1780, 1680, 1525, 1410, 1380. NMR spectrum (CF₃COOD) δ : 3.50 and 3.80(2H,ABq,J=18Hz), 5.51 (2H,br.s), 5.58 and 6.09(2H,ABq,J=14Hz), 7.96(1H,d.d, J=5Hz and 10Hz), 8.26(1H,d,J=2Hz), 8.40(1H,d,J=2Hz), 8.71(1H,d,J=10Hz), 9.00(1H,d,J=5Hz). TLC (Merck, Art 5715; solvent: acetonitrile:formic acid:water = 3:1:1), Rf = 0.5. (3) To 20 ml of dichloromethane, are added 2-(5-amino-1,2,4-thiadiazol-3-yl)-2(Z)-2-methoxyiminoacetic acid (202 mg), N-hydroxybenztriazole (153 mg) and dicyclohexylcarbodiimide (206 mg) and the suspension obtained is stirred for 60 minutes at room temperature. Insoluble material is filtered off and the filtrate is added to a solution of 445 mg of 7β-amino-3-[(imidazo[1,2-b]pyridazinium-1-yl)methyl]-3-cephem-4-carboxylate trifluoroacetate in 8 ml of dimethylacetamide and the mixture is stirred for 16 hours at room temperature. To the reaction mixture is added 30 ml of ether. After the ether layer is removed by decantation, the residue is dissolved in water and subjected to chromatography on a column of XAD-2®. The column is developed with ether and then with 20 % ethanol-water. The eluate containing the object compound is concentrated and the residue is lyophilized to give 0.2 g of the title compound. IR spectrum of the compound is the same as that in Example 13. Example 29 7β-[2-(5-Amino-1,2,4-thiadiazol-3-yl)-2(Z)-methoxyiminoacetamido]-3-[(imidazo[1,2-b]pyridazinium-1-yl)methyl]-3-cephem-4-carboxylate. (1) To a solution of 218 mg of phosphorous pentachloride in 3 ml of methylene chloride, 202 mg of 2-(5-amino-1,2,4-thiadiazol-3-yl)-2(Z)-methoxyiminoacetic acid is added under cooling at -20°C with stirring and the mixture is stirred for half an hour at -20°C and for two hours at -5°C. The reaction mixture is concentrated under reduced pressure and the residue is triturated with 10 ml of hexane. The precipitate is collected by filtration to give 2-(5-amino-1,2,4-thiadiazol-3-yl)-2(Z)-methoxyiminoacetyl chloride hydrochloride. (2) 7β-Amino-3-[(imidazo[1,3-b]pyridazinium-1-yl)methyl]-3-cephem-4-carboxylate hydrochloride (354 mg) is dissolved in a mixture of 10 ml each of acetone and water under ice-cooling. After addition of 504 mg of sodium bicarbonate and one minute's stirring, the whole amount of 2-(5-amino-1,2,4-thiadiazol-3-yl)-2(Z)-methoxyiminoacetyl chloride hydrochloride obtained above is added and the mixture is stirred energetically for 20 minutes under ice-cooling. To the reaction mixture is added 20 ml of ethyl acetate and the upper layer is removed and the lower layer is washed twice with each 20 ml of ethyl acetate. The aqueous layer is separated and acidified with concentrated hydrochloric acid to pH 1 and washed with a mixture of 20 ml of methyl ethyl ketone and 10 ml of ethyl acetate and then with a mixture of each 10 ml of methyl ethyl ketone and ethyl acetate. Then, the aqueous layer is adjusted to pH 3 and chromatographed on a column of MCI gel, CHP 20P® (Mitsubishi Kasei, Japan), first, with water and then with aqueous acetonitrile. Fractions containing the object compound are combined and concentrated and the residue is lyophilized to give the title compound. TLC (Silica gel, Merck, Art 5715; Solvent: acetonitrile:water = 4:1): Rf=0.26. 1765, 1660, 1610, 1520. Example 30 7β-[2-(5-Amino-1,2,4-thiadiazol-3-yl)2(Z)-methoxyiminoacetamido]-3-[(imidazo[1,2-b]pyridazinium-1-yl)methyl]-3-cephem-4-carboxylate. 30-1) By the procedure of Example 29 but using 606 mg of triethylamine instead of the 504 mg of sodium bicarbonate, the title compound is obtained and identified as such by comparing its IR-, NMR-spectra, Rf-value in TLC and retention time in HPLC with those of the product obtained in Example 29. 30-2) By the procedure of Example 29 but using tetrahydrofuran instead of the acetone, the title compound is obtained. 30-3) By the procedure of Example 29 but using acetonitrile instead of the acetone, the title compound is obtained. Example 31 7β-[2-(5-Amino-1,2,4-thiadiazol-3-yl)-2(Z)-methoxyiminoacetamidoo]-3-[(imidazo[1,2-b]pyridazinium-1-yl)methyl]-3-cephem-4-carboxylate 7β-Amino-3-[(imidazo[1,2-b]pyridazinium-1-yl)methyl]-3-cephem-4-carboxylate hydrochloride (354 mg) is dissolved in a mixture of 4 ml of dimethylformamide and 1.11 g of tributylamine and the solution is cooled to -20°C. To this, 2-(5-amino-1,2,4-thiadiazol-3-yl)-2(Z)-methoxyiminoacetyl chloride hydrochloride (the whole amount of it prepared as in Example 29 using the same amounts of the starting material and reagents) is added and the mixture is stirred for ten minutes at -20°C to -10°C and then for another ten minutes at -10°C to 0°C. The reaction mixture is diluted with 60 ml of ethyl acetate and then treated with 2 ml of 4N solution of hydrogen chloride in ether. The precipitate separated is collected by filtration, washed with 10 ml of ethyl acetate and 20 ml of methylene chloride and then suspended in 5 ml of water. The mixture is adjusted to pH 3 and chromatographed on a column of MCI gel, CHP-20P® (Mitsubishi-Kasei, Japan). The column is developed first with water and then with aqueous acetonitrile and fractions containing the object compound are combined and concentrated and the residue is lyophilized to give the title compound. The product obtained showed identical IR-, NMR-spectra, RF-value in TLC and retention time in HPLC with those of the product obtained in Example 29. Example 32 7β-[2-(5-Amino-1,2,4-thiadiazol-3-yl)-2(Z)-methoxyiminoacetamido]-3-[(imidazo[1,2-b]pyridazinium-1-yl)methyl]-3-cephem-4-carboxylate. 32-1) By the procedure of Example 31 but using dimethylacetamide instead of the dimethylformamide, the title compound is obtained and identified with it by means of physico-chemical measurements. 32-2) By the procedure of Example 31 but using triethylamine instead of the tributylamine, the title compound is obtained.

Claims: Claims for the following Contracting States : BE, CH, DE, FR, GB, IT, LI, LU, NL, SE A compound of the formula; wherein R¹ is an amino group or an amino group protected by a conventional protective group; R³ is a hydrogen atom or a hydrocarbon residue optionally substituted by one to three of hydroxyl, C₁₋₆ alkyl, C₂₋₆ alkenyl, C₂₋₆ alkynyl, C₃₋₁₀ cycloalkyl, C₅₋₆ cycloalkenyl, C₆₋₁₀ aryl, C₇₋₁₉ aralkyl, a 5 to 8-membered ring containing one to four heteroatoms of nitrogen atom which may optionally be oxidized, oxygen atom, sulfur atom or a fused ring thereof, C₁₋₆ alkoxy, C₃₋₁₀ cycloalkyloxy, C₆₋₁₀ aryloxy, C₇₋₁₉ aralkyloxy, thiazolyloxy, mercapto, C₁₋₆ alkylthio, C₃₋₁₀ cycloalkylthio, C₆₋₁₀ arylthio, C₇₋₁₉ aralkylthio, thiazolylthio, amino, mono-C₁₋₆ alkylamino, di-C₁₋₆ alkylamino, tri-C₁₋₆ alkylammonium, C₃₋₁₀ cycloalkylamino, C₆₋₁₀ arylamino, C₇₋₁₉ aralkylamino, thiazolylamino, thiadiazolylamino, cyclic amino, azido, nitro, halogen, cyano, carboxyl, C₁₋₁₀ alkoxy-carbonyl, C₆₋₁₀ aryloxycarbonyl, C₇₋₁₉ aralkyloxy-carbonyl, benzoyl, naphthoyl, phthaloyl, phenylacetyl, C₁₋₆ alkanoyl, C₃₋₅ alkenoyl, benzoyloxy, naphthoyloxy, phenylacetoxy, C₂₋₆ alkanoyloxy, C₃₋₅ alkenoyloxy, carbamoyl, N-methylcarbamoyl, N,N-dimethylcarbamoyl, N-ethylcarbamoyl, N,N-diethylcarbamoyl, N-phenylcarbamoyl, N-acetylcarbamoyl, N-benzoylcarbamoyl, N-(p-methoxy-phenyl)carbamoyl, pyrrolidinocarbonyl, piperidinocarbonyl, piperazinocarbonyl, morpholinocarbonyl, thiocarbamoyl, N-methylthiocarbamoyl, N-phenylthiocarbamoyl, carbamoyloxy, N-methylcarbamoyloxy, N,N-dimethylcarbamoyloxy, N-ethylcarbamoyloxy, N-phenylcarbamoyloxy, phthalimido, C₁₋₆ alkanoylamino, benzamido, naphthoylamido, phthalimido, carboxyamino, C₁₋₁₀ alkoxy-carboxamido, C₆₋₁₀ aryloxycarboxamido or C₇₋₁₉ aralkyloxy-carboxamido; Z is S, S -> O, O or CH₂; R⁴ is a hydrogen atom, methoxy group or formamido group; R¹³ is a hydrogen atom, methyl group, hydroxyl group or halogen atom and A⁺ is an imidazolium-1-yl group forming a fused ring at the 2,3- or 3,4-position that is optionally substituted by one or two of hydroxyl group, hydroxy C₁₋₆ alkyl group, C₁₋₆ alkyl group, C₂₋₆ alkenyl group, C₂₋₆-alkynyl group, C₄₋₆ alkadienyl group, C₃₋₁₀ cycloalkyl group, C₅₋₆ cycloalkenyl group, C₃₋₁₀ cycloalkyl C₁₋₆ alkyl group, C₆₋₁₀ aryl group, C₇₋₁₂ aralkyl group, di-C₆₋₁₀ aryl-methyl group, tri-C₆₋₁₀ arylmethyl group, a 5 to 8-membered ring containing one to four heteroatoms of nitrogen atom which may optionally be oxidized, oxygen atom, sulfur atom or a fused ring thereof, C₁₋₆ alkoxy group, C₁₋₆ alkoxy C₁₋₆ alkyl group, C₃₋₁₀ cycloalkyloxy group, C₆₋₁₀ aryloxy group, C₇₋₁₉ aralkyloxy group, mercapto group, mercapto C₁₋₆ alkyl group, sulfo group, sulfo C₁₋₆ alkyl group, C₁₋₆ alkylthio group, C₁₋₆ alkylthio C₁₋₆ alkyl group, C₃₋₁₀ cycloalkylthio group, C₆₋₁₀ arylthio group, C₇₋₁₉ aralkylthio group, amino group, amino C₁₋₆ alkyl group, mono-C₁₋₆ alkylamino group, di-C₁₋₆ alkylamino group, mono-C₁₋₆ alkylamino C₁₋₆ alkyl group, di-C₁₋₆ alkylamino C₁₋₆ alkyl group, C₃₋₁₀ cycloalkylamino group, C₆₋₁₀ arylamino group, C₇₋₁₉ aralkylamino group, cyclic amino group, cyclic amino C₁₋₆ alkyl group, cyclic amino C₁₋₆ alkylamino group, azido group, nitro group, halogen atom, halogeno C₁₋₆ alkyl group, cyano group, cyano C₁₋₆ alkyl group, carboxyl group, carboxy C₁₋₆ alkyl group, C₁₋₁₀ alkoxy-carbonyl group, C₁₋₁₀ alkoxy-carbonyl C₁₋₆ alkyl group, C₆₋₁₀ aryloxy-carbonyl group, C₇₋₁₉ aralkyloxycarbonyl group, benzoyl, naphthoyl, phthaloyl, phenylacetyl, C₁₋₆ alkanoyl group, C₂₋₆ alkanoyl C₁₋₆ alkyl group, C₃₋₅ alkenoyl group, benzoyloxy, naphthoyloxy, phenylacetoxy, C₂₋₆ alkanoyloxy group, C₂₋₆ alkanoyloxy C₁₋₆ alkyl group, C₃₋₅ alkenoyloxy group, carbamoyl C₁₋₆ alkyl group, carbamoyl, N-methylcarbamoyl, N,N-dimethylcarbamoyl, N-ethylcarbamoyl, N,N-diethylcarbamoyl, N-phenylcarbamoyl, N-acetylcarbamoyl, N-Benzoylcarbamoyl, N-(p-methoxyphenyl)carbamoyl, thiocarbamoyl, N-methylthiocarbamoyl, N-Phenylthiocarbamoyl, carbamoyloxy, N-methylcarbamoyloxy, N,N-dimethylcarbamoyloxy, N-ethylcarbamoyloxy, N-phenylcarbamoyloxy, carbamoyloxy C₁₋₆ alkyl group, C₁₋₆ alkanoylamino group, benzamido, naphthoylamido, phthalimido, sulfonamido group, carboxyamino group, C₁₋₁₀ alkoxycarboxamido group, C₆₋₁₀ aryloxy-carboxamido group, and C₇₋₁₉ aralkyloxy-carboxamido group, or a physiologically or pharmaceutically acceptable salt or ester thereof. The compound according to claim 1 wherein the optionally substituted hydrocarbon residue for R³ is C₁₋₃ alkyl group which may be substituted by halogen atom, hydroxyl group, C₁₋₆ alkoxy group, carboxyl group, C₁₋₆ alkoxycarbonyl group or cyano group, the number of the substituents being one to three. The compound according to claim 1 wherein Z is S; R⁴ is hydrogen atom; and R¹³ is hydrogen atom. The compound according to claim 1, wherein A ⊕ is an imidazo[1,5-a]pyridinium-2-yl group which is substituted by C₁₋₆ alkyl group, halogen atom or cyano group, the number of the substituents being one to two. The compound according to claim 1, wherein R¹ is amino group; R³ is C₁₋₃ alkyl group which may be substituted by one or two substituent(s) as defined in claim 1; and A ⊕ is an imidazo[1,2-a]pyridinium-1-yl group which is substituted by fluorine or cyano group. The compound according to claim 1 wherein A ⊕ is an optionally substituted imidazolium-1-yl group having at the 2,3- or 3,4-position a 5 to 6 membered aromatic heterocyclic ring condensed herewith, that is optionally substituted by one or two substituent(s) as defined in claim 1. The compound according to claim 1 wherein A ⊕ is an imidazo[1,2-a]pyridinium-1-yl, imidazo[1,5-a]pyridinium-2-yl or imidazo[1,2-b]pyridazinium-1-yl group, which may be substituted by one or two substituent(s) as defined in claim 1. The compound according to claim 1 wherein R¹ is amino group, R³ is C₁₋₃ alkyl group optionally substituted by halogen atom, hydroxy group, C₁₋₆ alkoxy group, carboxyl group, C₁₋₆ alkoxy-carbonyl group or cyano group, Z is S, R⁴ is hydrogen atom, R¹³ is hydrogen atom and A⁺ is an imidazo[1,2-a]pyridinium-1-yl, imidazo[1,5-a]pyridinium-2-yl or imidazo[1,2-b]pyridazinium-1-yl group which may be substituted by one or two substituent(s) as defined in claim 1. The compound according to claim 1, wherein A ⊕ is an imidazo[1,2-b]pyridazinium-1-yl group which may be substituted by C₁₋₆ alkyl, halogen, C₁₋₆ alkoxy, di-C₁₋₆ alkylamino di-C₁₋₆ alkylamino-C₁₋₆ alkylthio, or C₁₋₆ alkylthio, the number of the substituents being one to two. The compound according to claim 1, wherein A ⊕ is an imidazo[1,2-a]pyridinium-1-yl group which may be substituted by halogen, cyano, or di-C₁₋₆ alkylamino-C₁₋₆ alkyl, the number of the substituents being one to two. The compound according to claim 1 wherein R³ is C₁₋₃ alkyl group which may be substituted by carboxyl group or cyano group, the number of the substituents being one to three. The compounds according to claim 1, selected from 7β-[2-(5-amino-1,2,4-thiadiazol-3-yl)-2(Z)-methoxyiminoacetamido]-3-[(imidazo[1,2-b]pyridazinium-1-y1)methyl]-3-cephem-4-carboxylate; 7β-[2-(5-amino-1,2,4-thiadiazol-3-yl)-2(Z)-ethoxyiminoacetamido]-3-[(imidazo[1,2-b]pyridazinium-1-y1)methyl]-3-cephem-4-carboxylate; 7β-[2-(5-amino-1,2,4-thiadiazol-3-yl)-2(Z)-methoxyiminoacetamido]-3-[(7-methylimidazo[1,2-b]pyridazinium-1-y1)-methyl]-3-cephem-4-carboxylate; 7β-[2-(5-amino-1,2,4-thiadiazol-3-yl)-2(Z)-methoxyiminoacetamido]-3-[6-chloroimidazo[1,2-b]pyridazinium-1-yl)methyl]-3-cephem-4-carboxylate; 7β-[2-(5-amino-1,2,4-thiadiazol-3-yl)-2(Z)-methoxyiminoacetamido]-3-[(6-methoxyimidazo[1,2-b]pyridazinium-1-yl]-3-cephem-4-carboxylate; 7β-[2-(5-amino-1,2,4-thiadiazol-3-yl)-2(Z)-methoxyiminoacetamido]-3-[(6-dimethylaminoimidazo[1,2-b]pyridazinium-1-yl)methyl]-3-cephem-4-carboxylate; 7β-[2-(5-amino-1,2,4-thiadiazol-3-yl)-2(Z)-carboxymethoxyiminoacetamido]-3-[(imidazo[1,2-b]pyridazinium-1-yl)methyl]-3 -cephem-4-carboxylate mono-sodium salt; 7β-[2-(5-amino-1,2,4-thiadiazol-3-yl)-2(Z)-methoxyiminoacetamido]-3-[(6-(2-dimethylaminoethylthio)imidazo[1,2-b]pyridazinium-1-yl)methyl]-3-cephem-4-carboxylate dihydrochloride; 7β-[2-(5-amino-1,2,4-thiadiazol-3-yl)-2(Z)-methoxyiminoacetamido]-3-[(imidazo[1,2-a]pyridazinium-1-y1)methyl]-3-cephem-4- carboxylate; 7β-[2-(5-amino-1,2,4-thiadiazol-3-yl)-2(Z)-ethoxyiminoacetamido]-3-[(imidazo[1,2-]pyridinium-1-y1)methyl] -3-cephem-4- carboxylate; 7β-[2-(5-amino-1,2,4-thiadiazol-3-yl)-2(Z)-ethoxyiminoacetamido)-3-[(6-chloroimidazo[1,2-a]pyridinium-1-yl)methyl]-3-cephem-4-carboxylate; 7β-[2-(5-amino-1,2,4-thiadiazol-3-yl)-2(Z)-methoxyiminoacetamido]-3-[(6-cyanoimidazo[1,2-a]pyridinium-1-yl)methyl]-3-cephem-4-carboxylate; 7β-[2-(5-amino-1,2,4-thiadiazol-3-yl)-2(Z)-ethoxyiminoacetamido]-3-[(6-cyanoimidazo[1,2-a]pyridinium-1-y1)methyl]-3-cephem-4-carboxylate; 7β-[2-(5-amino-1,2,4-thiadiazol-3-yl)-2(Z)-carboxymethoxyiminoacetamido]-3-[(6-cyanoimidazo[1,2-a]pyridinium-1-yl)-methyl]-3-cephem-4-carboxylate and; 7β-[2-(5-amino-1,2,4-thiadiazol-3-yl)-2(Z)-methoxyiminoacetamido]-3-[(6-methylthioimidazo[1,2-b]pyridazinium-1-yl)methyl]-3-cephem-4-carboxylate dihydrochloride. A method for producing a compound as defined in claim 1 which comprises (1) reacting a compound of the formula: wherein the symbols are of the same meaning as defined above or a salt or ester thereof with carboxylic acid of the formula: or a salt or reactive derivative thereof, or (2) reacting a compound of the formula; wherein R⁵ is hydroxyl group, acyloxy group, carbamoyloxy group, substituted carbamoyloxy group or halogen atom and other symbols are of the same meaning as defined above, or a salt or ester thereof with an lmidazole compound of the formula A' (A' means an imidazole forming a condensed ring at the 2,3- or 3,4-position that is optionally substituted by one or two substituent(s) as defined above for A, or a salt thereof, or (3) reacting a compound of the formula: wherein the symbols are of the same meaning as defined above or a salt or ester thereof with a compound of the formula R 3'' OH wherein R 3'' is an optionally substituted hydrocarbon residue as defined above for R³, or a reactive derivative thereof. A pharmaceutical composition containing at least one of the compounds as defined in claim 1. Use of a compound as defined in claim 1 or a composition according to claim 14 for the preparation of a medicament useful as antibacterial agent. Claims for the following Contracting State : AT A method for producing a compound of the formula; wherein R¹ is an amino group which may be protected, R³ is hydrogen atom or a hydrocarbon residue optionally substituted by one to three of hydroxyl, C₁₋₆ alkyl, C₂₋₆ alkenyl, C₂₋₆ alkynyl, C₃₋₁₀ cycloalkyl, C₅₋₆ cycloalkenyl, C₆₋₁₀ aryl, C₇₋₁₉ aralkyl, a 5 to 8-membered ring containing one to four heteroatoms of nitrogen atom which may optionally be oxidized, oxygen atom, sulfur atom or a fused ring thereof, C₁₋₆ alkoxy, C₃₋₁₀ cycloalkyloxy, C₆₋₁₀ aryloxy, C₇₋₁₉ aralkyloxy, thiazolyloxy, mercapto, C₁₋₆ alkylthio, C₃₋₁₀ cycloalkylthio, C₆₋₁₀ arylthio, C₇₋₁₉ aralkylthio, thiazolylthio, amino, mono-C₁₋₆ alkylamino, di-C₁₋₆ alkylamino, tri-C₁₋₆ alkylammonium, C₃₋₁₀ cycloalkylamino, C₆₋₁₀ arylamino, C₇₋₁₉ aralkylamino, thiazolylamino, thiadiazolylamino, cyclic amino, azido, nitro, halogen, cyano, carboxyl, C₁₋₁₀ alkoxy-carbonyl, C₆₋₁₀ aryloxycarbonyl, C₇₋₁₉ aralkyloxy-carbonyl, benzoyl, naphthoyl, phthaloyl, phenylacetyl, C₁₋₆ alkanoyl, C₃₋₅ alkenoyl, benzoyloxy, naphthoyloxy, phenylacetoxy, C₂₋₆ alkanoyloxy, C₃₋₅ alkenoyloxy, carbamoyl, N-methylcarbamoyl, N,N-dimethylcarbamoyl, N-ethylcarbamoyl, N,N-diethylcarbamoyl, N-phenylcarbamoyl, N-acetylcarbamoyl, N-benzoylcarbamoyl, N-(p-methoxy-phenyl)carbamoyl, pyrrolidinocarbonyl, piperidinocarbonyl, piperazinocarbonyl, morpholinocarbonyl, thiocarbamoyl, N-methylthiocarbamoyl, N-phenylthiocarbamoyl, carbamoyloxy, N-methylcarbamoyloxy, N,N-dimethylcarbamoyloxy, N-ethylcarbamoyloxy, N-phenylcarbamoyloxy, phthalimido, C₁₋₆ alkanoylamino, benzamido, naphthoylamido, phthalimido, carboxyamino, C₁₋₁₀ alkoxy-carboxamido, C₆₋₁₀ aryloxy-carboxamido or C₇₋₁₉ aralkyloxy-carboxamido; Z is S, S -> O, O or CH₂; R⁴ is a hydrogen atom, methoxy group or formamido group; R¹³ is a hydrogen atom, methyl group, hydroxyl group or halogen atom and A⁺ is an imidazolium-1-yl group forming a fused ring at the 2,3- or 3,4-position that is optionally substituted by one or two of hydroxyl group, hydroxy C₁₋₆ alkyl group, C₁₋₆ alkyl group, C₂₋₆ alkenyl group, C₂₋₆-alkynyl group, C₄₋₆ alkadienyl group, C₃₋₁₀ cycloalkyl group, C₅₋₆ cycloalkenyl group, C₃₋₁₀ cycloalkyl C₁₋₆ alkyl group, C₆₋₁₀ aryl group, C₇₋₁₂ aralkyl group, di-C₆₋₁₀ aryl-methyl group, tri-C₆₋₁₀ arylmethyl group, a 5 to 8-membered ring containing one to four heteroatoms of nitrogen atom which may optionally be oxidized, oxygen atom, sulfur atom or a fused ring thereof, C₁₋₆ alkoxy group, C₁₋₆ alkoxy C₁₋₆ alkyl group, C₃₋₁₀ cycloalkyloxy group, C₆₋₁₀ aryloxy group, C₇₋₁₉ aralkyloxy group, mercapto group, mercapto C₁₋₆ alkyl group, sulfo group, sulfo C₁₋₆ alkyl group, C₁₋₆ alkylthio group, C₁₋₆ alkylthio C₁₋₆ alkyl group, C₃₋₁₀ cycloalkylthio group, C₆₋₁₀ arylthio group, C₇₋₁₉ aralkylthio group, amino group, amino C₁₋₆ alkyl group, mono-C₁₋₆ alkylamino group, di-C₁₋₆ alkylamino group, mono-C₁₋₆ alkylamino C₁₋₆ alkyl group, di-C₁₋₆ alkylamino C₁₋₆ alkyl group, C₃₋₁₀ cycloalkylamino group, C₆₋₁₀ arylamino group, C₇₋₁₉ aralkylamino group, cyclic amino group, cyclic amino C₁₋₆ alkyl group, cyclic amino C₁₋₆ alkylamino group, azido group, nitro group, halogen atom, halogeno C₁₋₆ alkyl group, cyano group, cyano C₁₋₆ alkyl group, carboxyl group, carboxy C₁₋₆ alkyl group, C₁₋₁₀ alkoxy-carbonyl group, C₁₋₁₀ alkoxy-carbonyl C₁₋₆ alkyl group, C₆₋₁₀ aryloxy-carbonyl group, C₇₋₁₉ aralkyloxycarbonyl group, benzoyl, naphthoyl, phthaloyl, phenylacetyl, C₁₋₆ alkanoyl group, C₂₋₆ alkanoyl C₁₋₆ alkyl group, C₃₋₅ alkenoyl group, benzoyloxy, naphthoyloxy, phenylacetoxy, C₂₋₆ alkanoyloxy group, C₂₋₆ alkanoyloxy C₁₋₆ alkyl group, C₃₋₅ alkenoyloxy group, carbamoyl C₁₋₆ alkyl group, carbamoyl, N-methylcarbamoyl, N,N-dimethylcarbamoyl, N-ethylcarbamoyl, N,N-diethylcarbamoyl, N-phenylcarbamoyl, N-acetylcarbamoyl, N-Benzoylcarbamoyl, N-(p-methoxyphenyl)carbamoyl, thiocarbamoyl, N-methylthiocarbamoyl, N-Phenylthiocarbamoyl, carbamoyloxy, N-methylcarbamoyloxy, N,N-dimethylcarbamoyloxy, N-ethylcarbamoyloxy, N-phenylcarbamoyloxy, carbamoyloxy C₁₋₆ alkyl group, C₁₋₆ alkanoylamino group, benzamido, naphthoylamido, phthalimido, sulfonamido group, carboxyamino group, C₁₋₁₀ alkoxycarboxamido group, C₆₋₁₀ aryloxy-carboxamido group, and C₇₋₁₉ aralkyloxy-carboxamido group, or a pharmaceutically acceptable salt or ester thereof, which comprises (1) reacting a compound of the formula: wherein the symbols are of the same meaning as defined above or a salt or ester thereof with carboxylic acid of the formula: or a salt or reactive derivative thereof, or (2) reacting a compound of the formula; wherein R⁵ is hydroxyl group, acyloxy group, carbamoyloxy group, substituted carbamoyloxy group or halogen atom and other symbols are of the same meaning as defined above, or a salt or ester thereof with an imidazole compound of the formula A' (A' means an imidazole forming a condensed ring at the 2,3- or 3,4-position that is optionally substituted by one or two substituent(s) as defined above for A, or a salt thereof, or (3) reacting a compound of the formula: wherein the symbols are of the same meaning as defined above or a salt or ester thereof with a compound of the formula R 3'' OH wherein R 3'' is an optionally substituted hydrocarbon residue as defined above for R³, or a reactive derivative thereof. The method according to claim 1 wherein the optionally substituted hydrocarbon residue for R³ is C₁₋₃ alkyl group which may be substituted by halogen atom, hydroxyl group, C₁₋₆ alkoxy group, carboxyl group, C₁₋₆ alkoxycarbonyl group or cyano group, the number of the substituents being one to three. The method according to claim 1 wherein Z is S; R⁴ is hydrogen atom; and R¹³ is hydrogen atom. The method according to claim 1, wherein A ⊕ is an imidazo[1,5-a]pyridinium-2-yl group which is substituted by C₁₋₆ alkyl group, halogen atom or cyano group, the number of the substituents being one to two. The method according to claim 1, wherein R¹ is amino group; R³ is C₁₋₃ alkyl group which may be substituted by one or two substituent(s) as defined in claim 1; and A ⊕ is an imidazo[1,2-a]pyridinium-1-yl group which is substituted by fluorine or cyano group. The method according to claim 1 wherein A ⊕ is an optionally substituted imidazolium-1-yl group having at the 2,3- or 3,4-position a 5 to 6 membered aromatic heterocyclic ring condensed herewith, that is optionally substituted by one or two substituent(s) as defined in claim 1. The method according to claim 1 wherein A ⊕ is an imidazo[1,2-a]pyridinium-1-yl, imidazo[1,5-a]pyridinium-2-yl or imidazo[1,2-b]pyridazinium-1-yl group, which may be substituted by one or two substituent(s) as defined in claim 1. The method according to claim 1 wherein R¹ is amino group, R³ is C₁₋₃ alkyl group optionally substituted by halogen atom, hydroxy group, C₁₋₆ alkoxy group, carboxyl group, C₁₋₆ alkoxy-carbonyl group or cyano group, Z is S, R⁴ is hydrogen atom, R¹³ is hydrogen atom and A⁺ is an imidazo[1,2-a]pyridinium-1-yl, imidazo[1,5-a]pyridinium-2-yl or imidazo[1,2-b]pyridazinium-1-yl group which may be substituted by one or two substituent(s) as defined in claim 1. The method according to claim 1, wherein A ⊕ is an imidazo[1,2-b]pyridazinium-1-yl group which may be substituted by C₁₋₆ alkyl, halogen, C₁₋₆ alkoxy, di-C₁₋₆ alkylamino di-C₁₋₆ alkylamino-C₁₋₆ alkylthio, or C₁₋₆ alkylthio, the number of the substituents being one to two. The method according to claim 1, wherein A ⊕ is an imidazo[1,2-a]pyridinium-1-yl group which may be substituted by halogen, cyano, or di-C₁₋₆ alkylamino-C₁₋₆ alkyl, the number of the substituents being one to two. The method according to claim 1 wherein R³ is C₁₋₃ al-kyl group which may be substituted by carboxyl group or cyano group, the number of the substituents being one to three. The method according to claim 1, for producing 7β-[2-(5-amino-1,2,4-thiadiazol-3-yl)-2(Z)-methoxyiminoacetamido]-3-[(imidazo[1,2-b]pyridazinium-1-y1)methyl]-3-cephem-4-carboxylate; 7β-[2-(5-amino-1,2,4-thiadiazol-3-yl)-2(Z)-ethoxyiminoacetamido]-3-[(imidazo[1,2-b]pyridazinium-1-y1)methyl]-3-cephem-4-carboxylate; 7β-[2-(5-amino-1,2,4-thiadiazol-3-yl)-2(Z)-methoxyiminoacetamido]-3-[(7-methylimidazo[1,2-b]pyridazinium-1-yl)methyl]-3-cephem-4-carboxylate; 7β-[2-(5-amino-1,2,4-thiadiazol-3-yl)-2(Z)-methoxyiminoacetamido]-3-[(6-chloroimidazo[1,2-b]pyridazinium-1-yl)methyl]-3-cephem-4-carboxylate; 7β-[2-(5-amino-1,2,4-thiadiazol-3-yl)-2(Z)-methoxyiminoacetamido]-3-[(6-methoxyimidazo[1,2-b]pyridazinium-1-yl)methyl]-3-cephem-4-carboxylate; 7β-[2-(5-amino-1,2,4-thiadiazol-3-yl)-2(Z)-methoxyiminoacetamido]-3-[6-dimethylaminoimidazo[1,2-b]pyridazinium-1-yl)methyl]-3-cephem-4-carboxylate; 7β-[2-(5-amino-1,2,4-thiadiazol-3-yl)-2(Z)-carboxymethoxyiminoacetamido]-3-[(imidazo[1,2-b]pyridazinium-1-yl)methyl]-3-cephem-4-carboxylate mono-sodium salt; 7β-[2-(5-amino-1,2,4-thiadiazol-3-yl)-2(Z)-methoxyiminoacetamido]-3-[(6-(2-dimethylaminoethylthio)imidazo[1,2-b]pyridazinium-1-yl)methy]-3-cephem-4-carboxylate dihydrochloride; 7β-[2-(5-amino-1,2,4-thiadiazol-3-yl)-2(Z)-methoxyiminoacetamido]-3-[(imidazo[1,2-a]pyridazinium-1-yl)methyl]-3-cephem-4- carboxylate; 7β-[2-(5-amino-1,2,4-thiadiazol-3-yl)-2(Z)-ethoxyiminoacetamido]-3-[(imidazo[1,2-]pyridinium-1-yl)methyl]-3-cephem-4- carboxylate; 7β-[2-(5-amino-1,2,4-thiadiazol-3-yl)-2(Z)-ethoxyiminoacetamido)-3-[(6-chloroimidazo[1,2-a]pyridinium-1-yl)methyl]-3-cephem-4-carboxylate; 7β-[2-(5-amino-1,2,4-thiadiazol-3-yl)-2(Z)-methoxyiminoacetamido]-3-[(6-cyanoimidazo[1,2-a]pyridinium-1-yl)methyl]-3-cephem-4-carboxylate; 7β-[2-(5-amino-1,2,4-thiadiazol-3-yl)-2(Z)-ethoxyiminoacetamido]-3-[(6-cyanoimidazo[1,2-a]pyridinium-1-yl)methyl]-3-cephem-4-carboxylate; 7β-[2-(5-amino-1,2,4-thiadiazol-3-yl)-2(Z)-carboxymethoxyiminoacetamido]-3-[(6-cyanoimidazo[1,2-a]pyridinium-1-yl)-methyl]-3-cephem-4-carboxylate and; 7β-[2-(5-amino-1,2,4-thiadiazol-3-yl)-2(Z)-methoxyiminoacetamido]-3-[(6-methylthioimidazo[1,2-b]pyridazinium-1-yl)methyl]-3-cephem-4-carboxylate dihydrochloride.

Inventors: FUJINO, MASAHIKO, KONDO, MASAHIRO, MIYAKE, AKIO
Applicants: TAKEDA CHEMICAL INDUSTRIES, LTD.
Application year: 1986
Main classification: C07D501
IPC codes: C07D505, A61P31, A61K31, C07D519, C07D463, C07D487, C07D471, C07D285, C07D277, C07D501