The invention concerns a syringe (1) comprising: a body including a cylindrical side wall (3) having an open upstream end with an inner annular rim (9) and a downstream end closed by a transverse wall provided with an orifice a shaft (10) equipped with a plunger (11) having at least two annular sealing lips (12, 13, 14) between which is defined at least one annular chamber (16, 17). The shaft, which can slide inside the body, defines inside the body an inner chamber designed to be at least partly filled with a content (18). Delivery passages (21) provided inside the body are configured to communicate said annular chamber of the plunger with the outside of the body or with the inner chamber of the body, when the plunger is abutting against the annular rim.