The invention comprises substituted tertiary amines of the general formula: <FORM:0945856/C2/1> wherein Y represents a hydrogen atom or a hydroxyl group, and when Y represents a hydrogen atom, R1 represents a hydrogen atom or an alkoxy group, R2 represents a hydrogen atom or an alkoxy group, and R3 represents a hydrogen atom or an alkoxy group, and when Y represents a hydroxyl group, R1 represents a hydrogen or halogen atom or an alkoxy group, R2 represents a hydrogen or halogen atom or an alkoxy group, and R3 represents a hydrogen atom or an alkoxy group, and wherein at least one of the phenyl rings carries at least one alkoxy group or halogen atom, and n, n1 and n11 represent integers from 1 to 5, and pharmaceutically acceptable substantially non-toxic acid addition salts and quaternary salts thereof, and the preparation of the above tertiary amines by reacting a compound of the general formula: <FORM:0945856/C2/2> wherein Y, R1, R2 and R3 and n, n1 and n11 have the above significance, with an excess of a complex metal hydride such as lithium aluminium hydride, an alkaline earth metal hydride, or an alkali metal hydride at an elevated temperature until the carbonyl group is reduced to a methylene group, and by reacting secondary anilines of the general formula: <FORM:0945856/C2/3> wherein R1, R2, R3 and Y have the above significance with a reactive derivative of a dialkylamino alkanol of the general formula: <FORM:0945856/C2/4> wherein n,n1 and n11 have the above significance and C represents a reactive substituent such as a halogen atom, preferably in the presence of an alkali metal amide, an alkali metal alcoholate, an alkali metal carbonate or an alkali metal hydroxide, and a process for the preparation of aniline compounds of the general formula: <FORM:0945856/C2/5> wherein R1, R2, R3, n, n1 and n11 have the above significance by reacting an epoxide of the general formula: <FORM:0945856/C2/6> wherein R3 has the above significance, with a dialkylamino-alkyl-aniline compound of the general formula: <FORM:0945856/C2/7> wherein R1, R2, n, n1 and n11 have the above significance.  The substituted tertiary amines of the first general formula in the case where Y represents a hydroxyl group may also be prepared by reducing secondary anilides of the general formula: <FORM:0945856/C2/8> wherein R1, R2, R3, n, n1 and n11 have the above significance and acyl represents a carboxylic acyl group, for example, with a complex metal hydride as previously referred to. Secondary anilides of the previous general formula wherein R1, R2, R3, n, n1, n11 and acyl have the significance indicated, are prepared by acylating dialkylaminoalkyl-anilines of the penultimate general formula above, wherein R1, R2, n, n1 and n11 have the significance indicated with the required O-acylated mandelic acids.  Secondary anilines of the third general formula above, wherein R1, R2, R3 and Y have the significance indicated, are prepared by reducing aralkoyl anilides of the general formula: <FORM:0945856/C2/9> wherein R1, R2, R3 and Y have the signifance previously indicated. N-(p-methoxyphenylacetyl) - N - diethylamino-ethyl-2,4-dimethoxy anilide is prepared by reacting 2,4-dimethoxy-aniline with diethylamino-ethyl chloride and treating the resulting N-diethylaminoethyl)-2,4-dimethoxy-aniline with p-methoxyphenylacetyl chloride.  N-diethylamino-ethyl-N-(1-phenyl - 2 - hydroxy-ethyl-1)-anisidine is formed as a by-product when styrene oxide is reacted with N-diethyl-aminoethyl-p-anisidine.  Therapeutic compositions having analgesic activity and which may be in the form of injectable solutions, tablets, pills, dragees, lozenges, powders, suppositories, emulsions, suspensions or syrups contain as the active ingredient a substituted tertiary amine of the first general formula above.