Inside a connector body (112, 114 300) of a medical connector providing a fluid flow conduit, a one-way valve (118) is fitted directly into one end of a stop valve (116) in a manner providing a fluid tight seal between these valves. The stop valve (116) prevents fluid flowing out of the end (111 311) of the connector body (112, 114 300) unless a complementary end of a separate device (not shown), typically a Luer lock connector, engages the end of the connector body and opens the stop valve (116). To facilitate manufacture and assembly, the one-way valve (118) and the stop valve (116) can be formed as parts of a single piece of elastomeric material, the parts being hingedly connected so that the one-way valve part (118) can be folded over to be fitted directly into the end of the stop valve part (116). A further possibility, also applicable when only a stop valve (116) is provided, is that the connector body (300) may be formed in one piece with a folding, snap fit closure (312).