A linear analysis of the stability of the flow in a laminar boundary layer under conditions of intensive interphase mass transfer, when high mass fluxes through the gas-liquid phase boundary induce secondary flows, is suggested. Essential interaction between flows in gas and liquid is considered in the case of a movable liquid surface. The critical Reynolds numbers are obtained at different intensities of non-linear mass transfer in a laminar boundary layer in the gas. The influence of the direction of the intensive interphase mass transfer on the hydrodynamic stability is analogous to the one in the case of motionless interface. The motion of the interface leads to a decrease of velocity gradients, which is the cause for increase in stability of the gas flow. Flow is stable at large Reynolds number in the liquid phase.