Numerical simulations of convection with strongly temperature-dependent viscosity suggest that non-Newtonian viscosity convection (dislocation creep) passes through three convective regimes similar to those observed for Newtonian viscosity convection (diffusion creep): the small viscosity contrast regime, the transitional regime and the stagnant lid regime. For realistic viscosity contrasts, mantle convection is in the stagnant lid regime characterized by formation of a very viscous, slowly creeping lid on top of an actively convecting mantle. This explains the tectonic style observed on the terrestrial planets and the Moon. On the other hand, this eliminates the possibility that the plates on Earth could be mobile due to non-Newtonian viscosity. The nature of the mobility of lithospheric plates on Earth has yet to be explained.¿ 1997 American Geophysical Union