Results are given about the parametric excitation of thermoelectric instability in a liquid semiconductor or an ionic melt layer subject to a harmonically time varying heat flux normal to its top open surface. First, it is shown that for a purely thermoelectric instability the ＇integer＇ disturbances are the most dangerous ones for the liquid quasiequilibrium. Then the boundaries of instability and characteristics of critical disturbances are found for the cases of coupled phenomena between thermoelectric effects and surface tension gradients and thermoelectric effects and buoyancy. Both ＇half-integer＇ and ＇integer＇ modes were studied. Qualitative and quantitative results are provided for the experimental observation of our predictions.