A flow system for medical lines includes a flow component having a main duct and at least one lateral tubular fitting with a female luer cone communicating with the main duct) through a valve. The valve includes a transverse diaphragm normally kept in fluid-tight contact against an annular valve seat of the lateral tubular fitting, which can be moved away from this into an opening position following upon insertion of a male luer-cone introducer of fluid into the lateral tubular fitting. The diaphragm is prearranged for being pushed into the opening position directly by the introducer, and the lateral tubular fitting is configured to couple in a fluid-tight way with the introducer before the latter comes into contact of thrust with the diaphragm.
