The influence of surface diffusion on the anisotropy of gas permeation through a two-layer nanoporous membrane has been studied. A model of gas transport in the bilayer membrane for the case of a gas flow composed of free molecular and surface flows has been constructed, wherein the scattering of molecules on the surface is defined by the "white noise" model. The influence of the surface diffusion on the anisotropy of gas permeability through the nanoporous bilayer membrane in the case of anisotropic scattering of gas molecules from the inner surface of the pores has been analyzed.