A port closure system, said system comprising: a port to establish communication between an interior volume that can receive a fluent substance and an exterior environment, the port having a laterally inwardly facing engaging surface; a valve including a flexible, resilient head extending across the port, the head having: an interior side facing the interior volume; an exterior side facing the exterior environment; at least one self-sealing slit through the head; confronting, openable portions along the slit to define a normally closed orifice in an unconstrained condition wherein the openable portions can move in a first direction toward the interior volume to an open orifice configuration and in a second direction toward the exterior environment to an open orifice configuration; and a laterally outwardly facing peripheral surface compressed laterally inwardly by engagement with the engaging surface to thereby impose a closing force on said self-sealing slit to increase the resistance of the normally closed orifice to opening in at least the second direction when the valve head is subjected to a pressure differential acting across the valve head; and characterised by an annular flange located to extend over at least a portion of the exterior side of said valve head to limit movement of the openable portions in the second direction. a port to establish communication between an interior volume that can receive a fluent substance and an exterior environment, the port having a laterally inwardly facing engaging surface; a valve including a flexible, resilient head extending across the port, the head having: an interior side facing the interior volume; an exterior side facing the exterior environment; at least one self-sealing slit through the head; confronting, openable portions along the slit to define a normally closed orifice in an unconstrained condition wherein the openable portions can move in a first direction toward the interior volume to an open orifice configuration and in a second direction toward the exterior environment to an open orifice configuration; and a laterally outwardly facing peripheral surface compressed laterally inwardly by engagement with the engaging surface to thereby impose a closing force on said self-sealing slit to increase the resistance of the normally closed orifice to opening in at least the second direction when the valve head is subjected to a pressure differential acting across the valve head; and characterised by an interior side facing the interior volume; an exterior side facing the exterior environment; at least one self-sealing slit through the head; confronting, openable portions along the slit to define a normally closed orifice in an unconstrained condition wherein the openable portions can move in a first direction toward the interior volume to an open orifice configuration and in a second direction toward the exterior environment to an open orifice configuration; and a laterally outwardly facing peripheral surface compressed laterally inwardly by engagement with the engaging surface to thereby impose a closing force on said self-sealing slit to increase the resistance of the normally closed orifice to opening in at least the second direction when the valve head is subjected to a pressure differential acting across the valve head; and characterised by an annular flange located to extend over at least a portion of the exterior side of said valve head to limit movement of the openable portions in the second direction.