The paper is devoted to the study of the simplest solution corresponding to the case of zero related phase velocity, when the temperature gradient and the vector of microacceleration are collinear and the thermocapillary forces are equalized with the floating forces. It is proved that in the first approximation the equilibrium state is unstable with respect to two and three-dimensional perturbations. The necessary and sufficient conditions of stability with respect to one-dimensional perturbations are found out. The stability of the simplest discontinuous solution corresponding to the case of an emulsion in equilibrium state and pure substance divided by plane interface is also considered.