We consider the dynamics of spreading of a small drop over a smooth solid surface. The analysis is concerned with complete wetting and accounts for capillary, viscous, and van der Waals effects, with two spreading geometries considered: cylindrical and axisymmetric. A complete description of the drop thickness, slope, and curvature profiles is provided. The model is not based on any fitting parameter, and the spreading laws are found to be in good agreement with published data obtained by different experimental techniques. The study evaluates the relative magnitudes of capillary, viscous, and disjoining-pressure effects and discusses the asymptotic form of the film profile and the existence of a singularity at the three-phase contact line. The model allows determination of the complete distribution of viscous dissipation in the whole drop, and the rate of viscous dissipation is related to the losses of the liquid drop free energy. Copyright 2000 Academic Press.