The onset of convective instability in the liquid phase epitaxy system is analyzed with linear stability theory. New stability equations are derived under the propagation theory, and the dimensionless critical time τc to mark the onset of the buoyancy-driven convection is obtained numerically. It is here found that the critical Rayleigh number Rac is 8000, below which the flow is unconditionally stable. For Ra>Rac the dimensionless critical time τc to mark the onset of a fastest growing instability is presented as a function of the Rayleigh number and the Schmidt number. Available numerical simulation results and theoretical predictions show that the manifest convection occurs starting from a certain time τo(>τc). It seems that during τc≤τ ≤τo secondary motion is relatively very weak.