Clamping device for a machine for duplicating keys, the clamping device comprising: - a body wherein two jaws (2, 3) are lodged able to firmly clasp between each other in the transverse sense according to a first axis a key to be decoded or a key to be coded, characterized by - one operation means, wherein actuation of the one operations means causes the two jaws, to move contemporaneously in their reciprocal approaching or spacing apart movements, - a portion which is arranged between said two jaws which can support said key, and which is solid to said body, - a bridge which is able to tighten said key against said portion of said body through a translation motion having direction parallel to a second axis orthogonal to said first axis, - wherein said bridge is at least partially engageable with said two jaws and the movement of said two jaws governs the approaching and tightening motion of said bridge to said key, - said two jaws (2, 3) are provided with respective inclined planes (2A, 3A) oriented with a predetermined inclination (2aa, 2bb) with respect to a central reference plane passing through said second axis and orthogonal to said first axis, - wherein said bridge is provided with two inclined planes (20A, 20B), each - one of said inclined planes (20A, 20B) of the bridge having the same inclination (2aa, 2bb) of a respective inclined plane (20A, 20B) of the jaws (2,3), each of said inclined planes (20A, 20B), - of the bridge being oriented towards said jaws, - and each one of said inclined planes (20A,20B) of the bridge being able to touch and slidingly engage said respective inclined plane (2A, 3A) of said two jaws. - a body wherein two jaws (2, 3) are lodged able to firmly clasp between each other in the transverse sense according to a first axis a key to be decoded or a key to be coded, characterized by - one operation means, wherein actuation of the one operations means causes the two jaws, to move contemporaneously in their reciprocal approaching or spacing apart movements, - a portion which is arranged between said two jaws which can support said key, and which is solid to said body, - a bridge which is able to tighten said key against said portion of said body through a translation motion having direction parallel to a second axis orthogonal to said first axis, - wherein said bridge is at least partially engageable with said two jaws and the movement of said two jaws governs the approaching and tightening motion of said bridge to said key, - said two jaws (2, 3) are provided with respective inclined planes (2A, 3A) oriented with a predetermined inclination (2aa, 2bb) with respect to a central reference plane passing through said second axis and orthogonal to said first axis, - wherein said bridge is provided with two inclined planes (20A, 20B), each - one of said inclined planes (20A, 20B) of the bridge having the same inclination (2aa, 2bb) of a respective inclined plane (20A, 20B) of the jaws (2,3), each of said inclined planes (20A, 20B), - of the bridge being oriented towards said jaws, - and each one of said inclined planes (20A,20B) of the bridge being able to touch and slidingly engage said respective inclined plane (2A, 3A) of said two jaws.