A connecting device in combination with a coaxial connector for a cooking range of an electric household appliance, wherein a thermocouple is to be connected to an assembly consisting of a safety electromagnet and a gas tap by means of the coaxial connector of the assembly comprising a conducting collar within which a male tip contact is arranged; the connecting device comprising: a tubular body made of non-conducting material and having a first end accommodating a female contact therein, connectable to a polarity wire of the thermocouple and to be coupled in use with the male tip contact, said first end being to be inserted in use into the collar of the coaxial connector to thus determine the coupling of the female contact to the male tip contact; and an electrically conducting, connecting element which may be connected to the ground wire of the thermocouple and carried radially on the outside of a central portion of the tubular body immediately adjacent to the first end, from which central portion the connecting element axially projects in cantilever fashion parallel to the first end so as to at least partially surround it; characterized in that, in combination: i)- the connecting element is elastically deformable in the radial direction and to circumferentially embrace with a radial clearance at least part of the collar of the coaxial connector when the female contact couples with the male tip contact; ii)- the connecting device further comprises a fastening element made of a non-conducting material and carried by the tubular body so as to be movable between a resting position, where it does not cooperate with the connecting element, and a working position, where the fastening element is received on the connecting element to radially close the same towards the first end of the tubular body and by such an amount that in use, when the female contact is coupled with the male tip contact, the connecting element is mechanically and electrically coupled with the collar; iii)- the fastening element being swingingly carried by a second end of the tubular body, opposite to the first end and transversally to a symmetry axis of the tubular body, in order to project in cantilever fashion from the second end and towards the first end, and to intercept the connecting element by means of a free end thereof, when it is in the working position. i)- the connecting element is elastically deformable in the radial direction and to circumferentially embrace with a radial clearance at least part of the collar of the coaxial connector when the female contact couples with the male tip contact; ii)- the connecting device further comprises a fastening element made of a non-conducting material and carried by the tubular body so as to be movable between a resting position, where it does not cooperate with the connecting element, and a working position, where the fastening element is received on the connecting element to radially close the same towards the first end of the tubular body and by such an amount that in use, when the female contact is coupled with the male tip contact, the connecting element is mechanically and electrically coupled with the collar; iii)- the fastening element being swingingly carried by a second end of the tubular body, opposite to the first end and transversally to a symmetry axis of the tubular body, in order to project in cantilever fashion from the second end and towards the first end, and to intercept the connecting element by means of a free end thereof, when it is in the working position.