The rheological properties of the upper mantle are examined on the basis of recent advances in the study of the rheology of partially melted rocks. The presence of a few percent liquid phase in the lowvelocity zone, which is indicated but not required by the geophysical evidence, does not affect the long-term creep properties of the material. Thus, while partial melting in the upper mantle can easily account for a variety of geodynamic processes, it cannot alter the rheology which is in all likelihood non-Newtonian. This conclusion is only apparently at odds with the most commonly accepted interpretation of postglacial isostatic rebound, which is taken to be compatible with a Maxwellian earth with Newtonian viscosity. It is pointed out here that neither the total strain, nor the time since deglaciation are such that the widespread assumption of steady-state rheology is necessarily justified. Under the assumption that transient creep, and not steady-state creep, governs the behaviour of the upper mantle during postglacial rebound, the inferred transient-creep viscosities are shown to be of the expected order of magnitude and to grade into the usually accepted steady-state viscosities at larger strains.