Abstract: A fastening device adapted in particular to be fastened on members having a grooved profile. The device has a main body, a control pin housed in engagement in this main body in an axial direction and moving with respect to this main body in order selectively to control the fastening or disengagement of this device, and a pressure member housed in the main body and moving with respect to the latter in a transverse direction. The pressure member is associated with the control pin such that, following the movement of the control pin with respect to the main body, the pressure member is moved in the transverse direction from and towards an operating position in which it projects from the main body.