The spreading kinetics of incompletely wetting liquids on porous substrates, highlighting the competition between composite interface spreading and liquid infiltration into the porous substrate are considered. The energetic impact of the surface porosity on the advancing of the contact line is modeled by using three idealized microtopologies associated with the kinetic behavior of the liquid in the pores. The results are used to modify a previously developed hydrodynamic spreading model to include the effects of substrate porosity. The results of a previously developed model for the depletion of a liquid droplet on a porous substrate are then used to consider the interaction between the spreading and depletion processes. It is predicted that, for a wide class of situations, a major portion of the spreading process will generally be completed before liquid drainage becomes significant. A contact angle hysteresis associated with spreading on a porous substrate is predicted to occur, with the advancing angle being larger than the receding angle; and an analogy is made with spreading on a rough or pitted substrate which provides a mechanism for contact angle hysteresis on such surfaces.