The bag side connector for a BIB package comprises: an element (10) having a longitudinal axis (12) and including a flange (14) with an upper and a lower face, wherein a first collar (16) protrudes from the upper face, so that a cylindrical chamber (18) is defined, a second collar (20) protrudes from the lower face, and the flange (14) has at least one through hole (22) in the area delimited by the second collar (20); and an internal valve device including an obturator (24) slidable along said axis (12) and a third collar (26) protruding from the lower face of the flange (14) coaxially and internally in respect of the second collar (20) and externally in respect of the area with at least one through hole (22), wherein said obturator (24) has a foot (30) suitable for contacting a distal edge (32) of the third collar (26) to form a leak-tight seal, and a top wall (34) from which an actuating pin (36) protrudes and extends through a center bore (38) of the flange (14). The connector further comprises an external valve device arranged in the chamber (18) and suitable for allowing/interrupting the fluid communication between the chamber (18) and the at least one (through hole (22) in dependence on the pressure existing in the chamber (18).