The invention concerns an elbow connector assembly (1) comprising a hollow elbow-shape structure (2) comprising an inner gas path (3), and an anti-asphyxia valve structure (7) comprising a flexible flap (8) arranged in the inner gas path (3) of the elbow-shape structure (2), as well as a respiratory mask (20) comprising such an elbow connector assembly (1), in particular a facial mask. The flexible flap (8) of the anti-asphyxia valve structure (7) is traversed by several holes (9) for venting expired gases to the atmosphere, during the exhalation phases of the patient.