Transfer stamping press fastening device for pneumatic pincers to be coupled to a stamping press transfer through at least one holder profile comprising a plurality of fastening supports (3a, 3b, 3c) for tubular support elements (4a, 4b) of said pincers, said fastening supports (3a, 3b, 3c) being capable of coupling to one of said holder profiles, and each of said fastening supports (3a, 3b, 3c) including a body that is adapted to receive at least one of said tubular elements (4a, 4b) and securing means (15a, 15b) to secure at least one of said tubular elements (4a, 4b) to the body of said fastening support (3a, 3b, 3c), characterised in that; - a first set of said fastening supports is configured so as to be removably coupled to the holder profile of said transfer press, each of said fastening supports including two body portions (12, 13), wherein the material of the body of said fastening supports comprises as the basic component, a technopolymer selected from a polyamide PA6, a polyamide PA66, a semi-aromatic polyamide, or polyphthalamide, and a polyphenylene sulfide, or a mixture thereof, and wherein both body portions (12, 13) define a mutual tightening surface configured to act as a mechanical stopper when a first tubular element is secured between both portions (12, 13), and in that; - a second set of said fastening supports (3b, 3c) each includes a body that is adapted to act as a joining element between said first tubular support element and a second outermost support tubular element associated with the same pincer, the first portion of said body defining a semi-open ring that is designed to receive the first tubular support element and the second portion of said body defining another semi-open ring that is designed to receive the second outermost tubular support element, wherein the material of the body of said fastening supports (3b, 3c) comprises as the basic component, a technopolymer selected from a polyamide PA6, a polyamide PA66, a semi-aromatic polyamide, or polyphthalamide, and a polyphenylene sulfide, or a mixture thereof, and wherein each of said semi-open rings (16a, 16b) include mutual tightening surfaces configured to act as a mechanical stopper when one of said tubular elements (4a, 4b) is secured in the interior thereof. - a first set of said fastening supports is configured so as to be removably coupled to the holder profile of said transfer press, each of said fastening supports including two body portions (12, 13), wherein the material of the body of said fastening supports comprises as the basic component, a technopolymer selected from a polyamide PA6, a polyamide PA66, a semi-aromatic polyamide, or polyphthalamide, and a polyphenylene sulfide, or a mixture thereof, and wherein both body portions (12, 13) define a mutual tightening surface configured to act as a mechanical stopper when a first tubular element is secured between both portions (12, 13), and in that; - a second set of said fastening supports (3b, 3c) each includes a body that is adapted to act as a joining element between said first tubular support element and a second outermost support tubular element associated with the same pincer, the first portion of said body defining a semi-open ring that is designed to receive the first tubular support element and the second portion of said body defining another semi-open ring that is designed to receive the second outermost tubular support element, wherein the material of the body of said fastening supports (3b, 3c) comprises as the basic component, a technopolymer selected from a polyamide PA6, a polyamide PA66, a semi-aromatic polyamide, or polyphthalamide, and a polyphenylene sulfide, or a mixture thereof, and wherein each of said semi-open rings (16a, 16b) include mutual tightening surfaces configured to act as a mechanical stopper when one of said tubular elements (4a, 4b) is secured in the interior thereof.