Numerical models of mantle convection using the Boussinesq, extended Bousinessq and anelastic-liquid approximation are compared. For steady state solutions there is good quantitative agreement between the results if they are scaled in a proper way. Time-dependent extended Boussinesq and anelastic-liquid flows show only qualitative agreement, the main difference being a distortion of timescale. Compressibility induces an asymmetry in the structure of upper and lower boundary layers that cannot be observed in Boussinesq fluids. ¿ American Geophysical Union 1989