Surface flow plays an important role in phenomena of gas or vapor transport in mesoporous pellets or membranes, which are of considerable practical interest; but a satisfactory unified formulation of surface flow over the whole applicable pressure range is as yet lacking. In analogy with gas phase flow (which varies from diffusive at low, to viscous at high, pressures), surface transport varies from diffusive, in the dilute monolayer region, to hydrodynamic, when the adsorbate is in the form of multimolecular layers or liquid condensate. Transport in these cases has been formulated in terms of a Fick surface diffusion coefficient or a hydrodynamic surface permeability respectively. We demonstrate here that attempts which have been made to extend each one of these formulations into the region of the other do not lead to physically acceptable results. We further show that an irreversible thermodynamic approach leads to the desired unified formulation of a "thermodynamic" diffusion coefficient, which appears to vary smoothly between the Fick value at infinite dilution and the value derived from the liquid permeability of the porous medium.