Abstract: A hydraulic shock absorber equipped with a leading stop, comprising a piston (4) sliding inside a body (2) for the purpose of shock absorption. The piston (4) moves a sleeve (10) which is disposed towards the front and provided with axially-distributed holes (18), and, at the shock absorber end-of-stroke, the sleeve fits around a stationary chamber (12) that gradually closes the holes (18), thereby reducing the cross-section through which fluid can flow into the sleeve (10). The chamber (12) comprises additional holes (40a, 40b) and said chamber (12) receives a moving gate (42) therein, which, depending on its position, either closes or opens the additional holes (40a, 40b).