Nanoparticles disclosed in the invention comprise a dextran-coated crystalline structure of cerium oxide wherein tetravalent Ce4+ predominates over trivalent Ce3+ and wherein said nanoparticles have a diameter of approximately from 3 to 5 nm. The nanoparticles exhibit both superoxide dismutase activity and catalase activity in an environment having a substantially neutral or acidic pH. The nanoparticles may be used to make and may be contained in a medication. The subject nanoparticles are useful in a method of promoting a cytotoxic anti-invasive effect on squamous tumor cells and inhibit tumor invasiveness.
