The transient buoyancy, thermocapillary, and buoyancy-thermocapillary convection in two superposed immiscible liquid layers in a finite cavity with side heating has been studied in the laminar regime by solving the complete two-dimensional Navier-Stokes and energy equations using the spline integration method. The development of the flow and temperature field as well as the velocity, interface vorticity, and heat transfer in both layers has been evaluated. Oscillatory behavior has been observed at high Rayleigh numbers and Marangoni numbers for moderate Prandtl numbers. The behavior of the heat transfer between the two layers through the interface separating them has been found to be particularly interesting, with large heat transfer rates occurring across the interface near the end walls at high Rayleigh numbers.