Transport of liquid water in a fuel cell gas diffusion layer is analyzed using capillary network modeling in which the mobility of both liquid and gas phases is considered to examine two distinct multiphase flow regimes: displacement and co-current flows. The simulations utilize a modified invasion percolation with trapping algorithm, and the capillary network consists of throats of different radii to account for the local heterogeneities of the porous media. Both displacement and two-mobile phase flow are solved, with inlet boundary condition for two-mobile phase flow prescribed through a discrete sequence of alternating phases entering the network. For both flow types (displacement and two-mobile phase), the cases studied range from capillary force controlled, where the maximum distance between two throats filled consecutively is equal to the network size, to viscous force controlled, where the maximum distance is set so as not to exceed some predefined value that is less than the network size. The maximum distance determines the distribution of phases; phase entrapment, percolation, and channeling are observed during the spread of phases for distinct flow conditions. Once a distribution of phases is obtained, we calculate saturation, relative permeabilities, and the capillary pressure at the interface between the phases; we also determine the dependence of these transport parameters on medium heterogeneity and cluster size. Finally, the changes of relative permeability and capillary pressure as a function of saturation are compared for displacement and two-mobile phase flow. (C) 2010 Elsevier B.V. All rights reserved.