A connector system for medical fluid administration has a female connection member, which can act as an access port for a container of medical fluid, and a male connection member, for accessing the container of medical fluid. The female connection member defines a sheath for receiving a portion of the male connection member and this sheath is spanned at one end by a septum, which acts to close the container of medical fluid. A lumen is defined through the male connection member to allow passage of fluid therethrough. The septum has a central region and a peripheral region, the central region being of substantially greater thickness than the peripheral region. The male connection member comprises means for rupturing the peripheral region of the septum when it is received in the female connection member to form a connection.
