A non-linear integral rheological model consistent with general creep theory and laboratory studies of rock creep is proposed to describe the rheology of the Earth's mantle. This model is universal, i.e., relevant to all strains, stresses and timescales. For constant stresses the model behaves like a power law non-Newtonian fluid. However, the model differs significantly if stresses change with time, because it has a memory, in contrast with the power law fluid model. A linear anisotropic integral rheological law that relates stress perturbation to strain perturbation is obtained for small-strain flows superimposed on a basic steady large-strain convective flow in the mantle. The rheological parameter in this law depends on the basic flow. The small-strain deformations associated with seismic waves and postglacial rebound are considered. In a pure power law fluid the effective viscosity associated with the convective flow is equal to the effective viscosity associated with postglacial rebound, whereas in the proposed model, the effective convective viscosity is about three orders of magnitude larger than the effective postglacial viscosity, at least for the lower mantle. ¿American Geophysical Union 1991