A combination membrane having both gas barrier properties and selective oxygen-absorbing and -carrying capability was prepared by complexing poly(vinylidene dichloride-co-vinylimidazole) and meso-tetrakis(alpha,alpha,alpha,alpha-o-pivalamidophenyl)porphyrin (CoP). The vinylidene dichloride copolymer was selected because of its low physical gas permeability and its dense and tough thin-membrane formability even after the CoP complexation. Oxygen permeation was selectively facilitated with the CoP carrier fixed in the membrane, and high oxygen permselectivity (facilitation factor > 25, oxygen/nitrogen permselectivity > 100, permeability 10(-10) cm(3) (STP) cm cm(-2) s(-1) cmHg(-1)) was observed, e.g., for the membrane containing > 20 wt % CoP at an upstream oxygen partial pressure of 0.5 cmHg. The facilitated oxygen transport was properly analyzed by a dual-mode model to give permeation parameters of the membrane such as the postulated diffusion coefficient of oxygen hopping via the fixed CoP carrier (D-C). D-C was inversely proportional to the average distance between the CoP carrier sites.