The onset time of natural convection driven by buoyancy forces and surface tension gradients is analysed theoretically in the initially quiescent horizontal fluid layers. The fluid layers experience the rapid evaporative cooling at the upper free surfacce. For this system, the stability analysis is conducted on the basis of the propagation theory that considers the time-dependent properties of disturbances and the nonlinear base temperature profiles. The onset time of natural convection has been governed by the Rayleigh number and the Maragoni number which represent the buoyancy-force and surface-tension effects, respecti- vely. The buoyancy forces and surface-tension gradients reinforce eaach other to induce na- tural convection. The results of the present analysis explain the experimental data of propanolreasonably.