Catalyst compositions include finely divided nanoscale particles of at least one supported oxide selected from among zirconium oxide, titanium oxide or a mixed zirconium/titanium oxide deposited onto an alumina-based or aluminum-oxyhydroxide-based support, wherein, after calcination for 4 hours at 900° C., the at least one support oxide is in the form of nanoscale particles deposited onto the support, the size of said particles being at most 10 nm when the at least one supported oxide is based is zirconium oxide and being at most 15 nm when the at least one supported oxide is titanium oxide or a mixed zirconium/titanium oxide; such catalyst compositions are especially useful for the selective reduction of NOx.