A needle-less flowing connector (10) includes a rotatable Luer housing (20), a Luer valve actuator (30), and a valve element (40) having a fluid passageway (44) which extends from an axially aligned end to an off center positioned end (48). Inter-engaged fingers (27), and grooves (47) prevent rotation of the valve element (40) with respect to the housing (20). An annular bulge (39), and groove (29) prevent withdrawal of the valve actuator (30) from the housing (20). An inter-engaged extending finger (25), and diametrically spaced grooves (35) position the valve in an open or closed position within the housing. A swabbing elastomeric stopper (80) is affixed over the open female Luer end of the valve actuator (30) to provide a safety seal against back flow of bodily fluid when a flow line is disconnected. The stopper (80) may be configured to provide a single or double seal.