The conditions and the critical time of transition from the diffusion mode to the convective mode of unsteady evaporation from a horizontal liquid layer into the stagnant gas layer over it were determined both theoretically and experimentally. It was shown that the diffusion evaporation mode loses its stability at the critical time if the molecular weight of the evaporating liquid is smaller than that of the gas in contact with this liquid. There emerges convection, which considerably raises the evaporation rate. Based on the physical notions of the mechanism of the vapor transfer in the supercritical region, a relation was proposed for calculating the rate of this process to within a constant coefficient. A technique was elaborated for experimental determination of the evaporation dynamics as a function of the contact time, and experimental data were obtained. These data agree satisfactorily with the theory, which provided a unified description of the evaporation rate in all of the systems studied.