Low-frequency mechanical spectroscopy measurements were performed in fine-grained zirconia and alumina. In both cases, anelastic relaxation phenomena at high temperature (>1200 K) have been observed, which are found to be in close correlation with the creep behavior. More precisely, a more or less resolved mechanical loss peak is obtained, superimposed on a mechanical loss background and accompanied by a decrease in the shear modulus. Creep deformation in these materials occurs mainly by accommodated grain boundary sliding and the anelastic deformation seems to be related to local grain-sliding motion. In the case of zirconia, the mechanical loss spectra consist of a mechanical loss peak which continuously evolves into an exponential background. This behavior can be described in terms of a model of grain boundary sliding, lubricated by an intergranular amorphous phase, the viscosity of which may thus be estimated. The transition from peak to background could then give an account for the onset of microcreep in these materials. Effectively, the activation energy values as obtained for the spectra are in close agreement with the corresponding values obtained by creep tests, and also the same dependence on grain size is found. The spectra in alumina are similar to those in zirconia, but show a complex dependence on the grain size, and the activation energy values are higher than those determined by creep tests. In order to account for all the features of the observed spectra, a description of the grain boundary sliding mechanism in terms of motion of grain boundary dislocations is needed.