A clamp device for detachably fastening an accessory support element to hospital furniture, for instance to an operating table or the like, said clamp device comprising first and second clamping elements (1, 2) that are interconnected,, said clamp device being suitable to be detachably fastened to an accessory rail or the like of hospital furniture, such as an operating table, by means of first clamping elements, and an accessory support element being suitable to be detachably fastened to the clamp device by means of second clamping elements, wherein - the first clamping elements comprise a fastening frame provided with a channel that is C-shaped in cross-section, wherein the channel is suitable for installing the accessory rail or the like of hospital furniture, such as an operating table; the first clamping elements further comprising locking means provided in connection with the fastening frame and the channel for fastening and locking the frame and at the same time detachably fastening the clamp device to the accessory rail, - the second clamping elements comprise jaws, wherein in between the jaw elements (31, 32) of said jaws, there is a gap; the second clamping elements further comprising a space for the accessory support element provided in the gap; the second clamping elements further comprising a compression element for pressing the jaws (3; 31, 32) together and opening them for respectively fastening and detaching the accessory support element; - wherein the second clamping elements further comprise an adjusting element for adjusting the diameter (h) of the space, wherein said adjusting element is arranged in the jaws (3; 31, 32) at a second end of the jaw elements, and on a second side of the space, whereas the compression element is arranged in the jaws (3; 31, 32) at a first end of the jaw elements and on a first side of the space, characterized in that the compression element is realized as a screw and nut element and the first clamping elements further comprise a first and second frame part (10; 101, 102), wherein said second frame part is arranged as the nut element of the compression element. - the first clamping elements comprise a fastening frame provided with a channel that is C-shaped in cross-section, wherein the channel is suitable for installing the accessory rail or the like of hospital furniture, such as an operating table; the first clamping elements further comprising locking means provided in connection with the fastening frame and the channel for fastening and locking the frame and at the same time detachably fastening the clamp device to the accessory rail, - the second clamping elements comprise jaws, wherein in between the jaw elements (31, 32) of said jaws, there is a gap; the second clamping elements further comprising a space for the accessory support element provided in the gap; the second clamping elements further comprising a compression element for pressing the jaws (3; 31, 32) together and opening them for respectively fastening and detaching the accessory support element; - wherein the second clamping elements further comprise an adjusting element for adjusting the diameter (h) of the space, wherein said adjusting element is arranged in the jaws (3; 31, 32) at a second end of the jaw elements, and on a second side of the space, whereas the compression element is arranged in the jaws (3; 31, 32) at a first end of the jaw elements and on a first side of the space,