A process for making nanoparticles of biocompatible materials is described, wherein an aqueous reaction mixture comprising cerous ion, citric acid and ethylenediaminetetraacetic acid in a predetermined ratio, an oxidant, and water is provided along with temperature conditions to directly form, without isolation, a stable dispersion of cerium oxide nanoparticles. These biocompatible cerium oxide nanoparticles may be used to prevent and/or treat oxidative stress related diseases, such as stroke, relapse/remitting multiple sclerosis, chronic-progressive multiple sclerosis, amyotrophic lateral sclerosis, and ischemic reperfusion injury.