Driving device for driving the opening/closing sequence of multiple-member telescopic stabilizers for a self-propelled machine, said telescopic multiple-member stabilizers comprising a largest member or fixed member configured to be integral with the machine frame, one or more intermediate members and a smallest member or resting member which bears a foot at its free end, the device comprising at least an actuation cylinder/piston assembly arranged between the fixed member and the resting member, characterized in that the device further comprises: - a double cam hook having two cams (3a, 3c) each projecting from a respective side of a vertical wall of the intermediate member and idly pivoted about a pin provided on said wall of the intermediate member; - a first pin element, projecting externally from the wall of said resting member, selectively engageable with a first of said two cams (3a, 3c) in order to engage each other the intermediate member and the resting member during the extraction movement of the intermediate member and disengageable from said first cam when the intermediate member has reached its maximum extracted position; - a second pin element, projecting internally from the wall of said fixed member, selectively engageable with a second of said two cams (3a, 3c) in order to engage each other the intermediate member and the fixed member during the retraction movement of said resting member and disengageable from said second cam when the resting member has reached its maximum retraction position; - a longitudinal guide element provided on the inner wall of the fixed member and upon which a planar part of said second cam is able to slide for a first part of the extraction movement and for a last part of the retraction movement of the intermediate member, wherein said guide element has a length preset so that its supporting action towards said second cam ceases when the cam starts to engage said second pin element, causing said double cam hook to rotate. - a double cam hook having two cams (3a, 3c) each projecting from a respective side of a vertical wall of the intermediate member and idly pivoted about a pin provided on said wall of the intermediate member; - a first pin element, projecting externally from the wall of said resting member, selectively engageable with a first of said two cams (3a, 3c) in order to engage each other the intermediate member and the resting member during the extraction movement of the intermediate member and disengageable from said first cam when the intermediate member has reached its maximum extracted position; - a second pin element, projecting internally from the wall of said fixed member, selectively engageable with a second of said two cams (3a, 3c) in order to engage each other the intermediate member and the fixed member during the retraction movement of said resting member and disengageable from said second cam when the resting member has reached its maximum retraction position; - a longitudinal guide element provided on the inner wall of the fixed member and upon which a planar part of said second cam is able to slide for a first part of the extraction movement and for a last part of the retraction movement of the intermediate member, wherein said guide element has a length preset so that its supporting action towards said second cam ceases when the cam starts to engage said second pin element, causing said double cam hook to rotate.