The superplastic behavior of alumina-based nanostructured ceramics (Al2O3) is an important issue in the world of materials. The main body of this paper is an analysis of the creep behavior of polycrystals, with grain boundary sliding as the main deformation mechanism at high temperatures. Concomitant accommodation of grain shapes to preserve spatial continuity has a comparatively small effect on the strain rate. The constitutive equations for small deformations, relating strain and strain rate, derived from two models for grain sliding, are compared with the experimental data with their respective uncertainties. The data follow from experiments on the plastic deformation of alumina composites reinforced, on the one hand by graphene oxide, and on the other hand by carbon nanofibers sintered by SPS. The results show good agreement between experiment and theory for these advanced ceramics, particularly for one of the assumed models. The values obtained of xi(2) for model A were in the interval 0.0002-0.1189, and for model B were in the interval 0.000001-0.0561. The values obtained of R-2 for model A were in the interval 0.9122-0.9994, and for model B were in the interval 0.9586-0.9999. The threshold stress was between (3.05 center dot 10(-15)-25.68) MPa.