A hollow cone device for gripping attachments, essentially constituted by a bit-carrying socket (1) for blocking the member (2) to be fixed, prolonged by a securement element (3) in a support (4), such as a spindle or the like. The securement element is in the form of a screw-threaded element connected to the socket (1) and screwed into the support (4). The bit-carrying socket (1) comprises two radial recesses extending perpendicularly to its axis and in which are mounted two gripping bits (5) actuated simultaneously, to slide radially in a symmetrical manner, by a screw (6) maintained in translation by a stud screw (7) co-acting with a circular throat provided in the central region of the screw (6). An ejector (12) is guided in translation in a bore in the bit-carrying socket (1) and actuated by symmetrical pressure of the bits (5). The device also includes an element (15) for relative angular displacement between the bit-carrying socket (1) and the screw-threaded element.