Mass transport across two-dimensional nanopores is very essential to the porous graphene and other atomically thin membranes for gas separation. Due to the contribution of gas adsorption and diffusion over the two-dimensional surfaces, mass transport across graphene nanopores cannot be described only by the kinetic theory of gases. We show that the combination of the linear pressure-dependent direct flux, governed by the kinetic motion of gas molecules, and the nonlinear pressure-dependent surface flux, caused by the Langmuir isothermal adsorption characteristics of gas molecules on the two-dimensional surfaces, results in an overall nonlinear pressure dependence of the gas permeation flux through graphene nanopores. Based on the mass transport resistance network connecting the multiple molecular transport processes in direct flux and surface flux, a theoretical model that captures the pressure dependence of permeation flux is established, offering a possible avenue to predict the mass transport rates through the two-dimensional nanopores. (C) 2017 Elsevier Ltd. All rights reserved.