The issue concerning the dominant creep mechanism in mantle convection has been studied numerically with a rheology incorporating both linear and non-linear elements. We have employed a rheology suggested by the recently obtained melting temperature of lower-mantle constituents. For an effective Rayleigh number between 105 and 106 this type of strongly temperature and pressure-dependent rheology induces a circulation in the Earth's mantle, which is characterized by a sluggish type of flow in the lower mantle with a prevailing Newtonian character, while in the upper mantle much more vigorous flows are developed in a predominantly non-Newtonian rheology. ¿ American Geophysical Union 1996