The dependences of phase stability and solid state phase transitions on the crystallite size in ZrO2-10, 12 and 14 mol% Sc2O3 nanopowders are investigated by X-ray powder diffraction using a synchrotron source (S-XPD). The average crystallite sizes lie within the range of 35 to 100 nm, approximately. At room temperature these solid solutions were previously characterised as mixtures of a cubic phase and one or two rhombohedral phases, β and γ, with their fractions depending on composition and average crystallite sizes. In this study, it is shown that at high temperatures these solid solutions become cubic single-phased. The size-dependent temperatures of the transitions from the rhombohedral phases to the cubic phase at high temperature are determined through the analyses of a number of S-XPD patterns. These transitions were studied on cooling and on heating, exhibiting hysteresis effects whose relevant features are size and composition dependent.