In thermoconvection problems, it is generally assumed that the dissipative effects at the interface play a negligible role. In dimensionless form, the importance of this effect can be quantified by the interface viscosity number Vi. The purpose of this paper is to examine the effects of an interface viscosity on convective motions through two illustrative situations performed within a two-dimensional (2D) finite-difference code. In the first example, the upper fluid is passive while in the second example, one considers two superposed immiscible fluids in a closed rectangular cavity. The maximum surface velocity, the stream lines and the kinetic energy of the bulk flow are calculated for Vi-values varying between 0 and 10. For Vi greater than or equal to 1, it is shown that the interface viscosity has a non-negligible influence, particularly in the vicinity of the interface.