An automobile double acting shock absorber comprises an outer body (4) and a stem (3) with an end portion sliding within the outer body. The outer body delimits two chambers (8a, 8b) separated by a diaphragm (10) having ports (9) for a fluid. The chambers communicate with each other through valves (7) which are disposed at said end portion of the stem within the outer body (4) and are adapted for controlling the ports (9) in the diaphragm (10). The shock absorber comprises a device for continuously varying the operational characteristics when a centrifugal force exceeding a preset threshold value occurs. Such a device consists of a metal ring (15) adapted for translation within a chamber (14) delimited by said diaphragm (10) and a second diaphragm (12) having apertures (23) obstructable by the ring (15) during translation movement thereof.