This mechanism makes it possible to obtain in succession a fast approach stroke (C), and then a work stroke with a substantial developed stress, in operations such as riveting or marking, the work stroke being started as the tool (16) comes into contact with the part to be pressed (25). A control stem (4) and a body (9) are movable along one and the same axis (3), means such as a clack (31) providing for their non permanent locking. The stem (4) is integral with a primary piston (8) penetrating into a hydraulic circuit (10, 11) of the body (9); this circuit communicates, on the one hand, with an expansible casing (19) surrounding the body (9) and making it possible to block this body with respect to the frame (1), and on the other hand, with a chamber (12) in which a secondary piston (15), drawn back by a spring (18) and integral with tool (16), slides.