A process for making cerium-containing oxide nanoparticles includes providing an aqueous reaction mixture containing a source of cerous ion, optionally a source of one or more metal ions (M) other than cerium, a source of hydroxide ion, at least one monoether carboxylic acid nanoparticle stabilizer wherein the molar ratio of said monoether carboxylic acid nanoparticle stabilizers to total metal ions is greater than 0.2, and an oxidant at an initial temperature in the range of about 20°C to about 95°C. Temperature conditions are provided effective to enable oxidation of cerous ion to ceric ion, thereby forming a product dispersion of cerium-containing oxide nanoparticles, optionally containing one or more metal ions (M), Ce 1-x M x O 2-δ , wherein "x" has a value from about 0.0 to about 0.95. The nanoparticles may have a mean hydrodynamic diameter from about 1 nm to about 50 nm, and a geometric diameter of less than about 45 nm.