Flow systems for medical lines, in particular for haemodialysis, include a flow component having a main duct for a primary fluid 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 constituted by the bottom wall of a cup-shaped element made of elastically deformable material, the outer peripheral edge of which is normally kept in fluid-tight contact against an annular valve seat of the lateral tubular fitting. A male luer-cone introducer of secondary fluid can be inserted into the lateral tubular fitting with female luer cone to displace the transverse diaphragm into an open position. This arrangement may entail the risk of the valve being opened before the male luer-cone introducer provides a seal with the female luer cone of the tubular fitting, resulting in contamination and leakage of fluid. To address this, the diaphragm is prearranged for being pushed into the open position as a result of the direct contact with and thrust by the male luer-cone introducer, and the lateral tubular fitting is coupled in a fluid-tight way with the introducer before the latter comes into contact with and applies a thrust to the diaphragm.
