A linear stability analysis for a Be´nard problem with two layers is considered. The equations are not self‐adjoint. The system can lose stability to time‐periodic disturbances. For example, it is shown numerically that when the viscosities and coefficients of cubical expansion of the fluids are different, a Hopf bifurcation can occur, resulting in a pair of traveling waves or a standing wave. This may have application in the modeling of convection in the Earth’s mantle.