A process for making nanoparticles of biocompatible materials is described, wherein an aqueous reaction mixture comprising cerous ion, ethylenediaminedisuccinic acid, an oxidant, water, and optionally citric acid, is provided along with temperature conditions to directly form within the reaction mixture, a stable dispersion of cerium oxide nanoparticles. Biocompatible, nanoparticles comprised of cerium oxide, ethylenediaminedisuccinic acid, and optionally citric acid, are described. An increase in catalase-like enzyme activity is demonstrated by cerium oxide nanoparticles prepared with citric acid and ethylenediaminedisuccinic acid.