A valved male luer connector including an elastic hollow element (15) which encloses a tubular member (5) having an inlet portion (7) and an outlet portion (6). A collar (28) is axially displaceable causing a stretching deformation of the elastic hollow element (15) and opening the flow passage between the inlet portion (7) and the outlet portion (6) of the tubular member (5). A priming cap (30) is designed to be releasably connected to the casing (1) of the valved connector to provide stretching deformation of the elastic element (15) and keep the outlet portion (6) of the tubular member (5) in communication with the atmosphere through a liquid-impermeable barrier (34). This allows immediate connection to a female connector without having to prime the supply line of the medical liquid, since the priming is made ready by the presence of the cap applied in a removable manner to the body of the connector, and without the risk of liquid loss.
