Oscillatory behaviour in thermocapillary convection with buoyancy forces has been studied numerically for superposed immiscible liquid layers with a free surface, in which the lower layer consists of low-Prandtl-number fluid. Numerical solutions to the complete two dimensional Navier-Stokes and energy equations have been obtained using the spline integration method. Attention has been focused on flow instabilities of an oscillatory nature which appear to be induced by the buoyancy forces. An attempt to understand the origin of these instabilities and indications on how to reduce or even avoid them is made. The numerical results demonstrate that oscillatory flow in a single layer of low-Prandtl number fluid may transform to a steady state after encapsulation With a fluid of higher Prandtl number, even in the absence of Marangoni forces, except when the buoyancy and the Viscous forces in the upper layer are very small when compared with the lower one. The numerical experiments also demonstrate that the addition of the combined Marangoni forces to the gravitational convection plays an important role in suppressing oscillatory flow. (C) 1997 Elsevier Science Ltd.