A suction gripper device comprising a pipe for connecting a suction source to a suction gripper member, the pipe comprising a first channel formed by a downstream chamber (5) and by an upstream duct (7), a seat (9) being provided between the chamber (5) and the duct (7), a valve member (6) being mounted to move with clearance inside the chamber (5) between a bottom abutment (2a, 22) and the seat (9), and a second channel (10) forming a calibrated bypass in parallel with the first channel and bypassing the seat (9), being of section that is smaller than the section (S) of the clearance that exists in the chamber (5) between its inside surface and the outside surface of the valve member (6) that can move therein, wherein the second channel (10) is formed through the center of the valve member (6).