We apply the molecular kinetic theory of wetting to the relaxation of the dynamic contact angle during the spreading of liquid droplets on solid surfaces. Experimental data have been obtained for several solid-liquid combinations and are successfully fitted using the theory. Physical parameters are extracted and interpreted in terms of the microscopic characteristics of the liquid and the solid. We also show that droplet spreading and forced wetting can be described by the same equations. a comparison is made between the results obtained within the molecular-kinetic framework and those obtained with conventional hydrodynamic theory.