A syringe has a plunger (38) movable within a barrel (36) having an inner diameter and a gasket (44) arranged between the plunger and the inner wall (58) of the barrel. This syringe is useful both for injecting and for sucking. For this purpose the gasket (44) is movably arranged between sections (60, 62) of the plunger whose outer diameter is smaller than the inner diameter of the barrel. The gasket (44) itself has an outer salient section and an inner membranous section which sealingly encloses the plunger.