Thermal instability in a horizontal Newtonian liquid layer with rigid boundaries is investigated in the presence of vertical quasiperiodic forcing having two incommensurate frequencies and . By means of a Galerkin projection truncated to the first order, the governing linear system corresponding to the onset of convection is reduced to a damped quasiperiodic Mathieu equation. The threshold of convection corresponding to quasiperiodic solutions is determined in the cases of heating from below and heating from above. We show that a modulation with two incommensurate frequencies has a stabilizing or a destabilizing effect depending on the frequencies ratio . The effect of the Prandtl number in a stabilizing zone is also examined for different frequency ratios.