A process for making nanoparticles of biocompatible materials is described, wherein an aqueous reaction mixture comprising cerous ion, citric acid, an oxidant, and water, is adjusted to a predetermined range of pH, held at temperature conditions to directly form, without isolation, a stable dispersion of cerium oxide nanoparticles. Dispersions of these biocompatible cerium oxide nanoparticles exhibit self-life well in excess of one year, and may be used to prevent and/or treat disease or injury, such as oxidative stress related diseases and events.