A male reflux valve comprising in combination: a body comprising a distal body portion and a proximal body portion, said proximal body portion having a male connection for connection to an access device having a female connection; an elastomeric valve element operatively positioned within said distal body portion, said valve element including a slit; a core operatively positioned within said distal body portion to retain said valve element into sealing engagement with said distal body portion in an orientation with said slit 44 facing proximally; and characterized in that it further comprises: an actuator reciprocably retained within a generally circular cylindrical longitudinal bore of the proximal body portion; said actuator comprising a small-diameter distal portion, a large-diameter center portion and a small-diameter proximal portion, with a longitudinal bore extending therethrough for fluid flow therethrough; a retainer wall extending radially inwardly within said proximal body portion to retain said center portion in said proximal body portion; said small-diameter distal portion being_in engagement with said slit of said valve element to open said valve element when said proximal portion is engaged by the female connection of the access device, whereby moving said actuator distally causes a lip of said distal portion to open said slit and form a seal therearound to establish a bi-directional fluid path in the valve allowing fluid flow to and from the access device. a body comprising a distal body portion and a proximal body portion, said proximal body portion having a male connection for connection to an access device having a female connection; an elastomeric valve element operatively positioned within said distal body portion, said valve element including a slit; a core operatively positioned within said distal body portion to retain said valve element into sealing engagement with said distal body portion in an orientation with said slit 44 facing proximally; and characterized in that it further comprises: an actuator reciprocably retained within a generally circular cylindrical longitudinal bore of the proximal body portion; said actuator comprising a small-diameter distal portion, a large-diameter center portion and a small-diameter proximal portion, with a longitudinal bore extending therethrough for fluid flow therethrough; a retainer wall extending radially inwardly within said proximal body portion to retain said center portion in said proximal body portion; said small-diameter distal portion being_in engagement with said slit of said valve element to open said valve element when said proximal portion is engaged by the female connection of the access device, whereby moving said actuator distally causes a lip of said distal portion to open said slit and form a seal therearound to establish a bi-directional fluid path in the valve allowing fluid flow to and from the access device. an actuator reciprocably retained within a generally circular cylindrical longitudinal bore of the proximal body portion; said actuator comprising a small-diameter distal portion, a large-diameter center portion and a small-diameter proximal portion, with a longitudinal bore extending therethrough for fluid flow therethrough; a retainer wall extending radially inwardly within said proximal body portion to retain said center portion in said proximal body portion; said small-diameter distal portion being_in engagement with said slit of said valve element to open said valve element when said proximal portion is engaged by the female connection of the access device, whereby moving said actuator distally causes a lip of said distal portion to open said slit and form a seal therearound to establish a bi-directional fluid path in the valve allowing fluid flow to and from the access device.