A connector (3) which is applicable to a bag (1) for containing liquid solutions for medical or nutritional use comprises a coupling part (11) for coupling to an end of a small tube (2) projecting from the bag (1) and provided with an axial hole (5) closed by a pierceable inner membrane (6). The coupling part (11) includes two coaxial tubes (12, 13) which define an annular space (14) extending axially with a constant cross-section, into which said end of the small tube (2) is forcibly insertable by axial pressure.