Compositions suitable for use as oxidation catalysts essentially free from elements, or compounds thereof, of Group VIII of the Periodic Table, comprise an intimate mixture of oxides of at least three elements selected from Groups IIIa and IVa of the Periodic Table, including, of the total number of Group IIIa and IVa element atoms present, a) a total of at least 60% of atoms of at least one element X selected from cerium, zirconium, and hafnium, b) a total of at least 5% of atoms of at least one other element Y different from element X and selected from the variable valency elements titanium, cerium, praseodymium, and terbium; and c) a total of at least 5% of atoms of at least one element Z differing from X and Y and selected from Group IIIa elements. Such composition, and similar two component compositions wherein X and Y are both cerium, have, after heating for 8 hours at 1200.degree. C., a BET surface area of at least 1 m.sup.2 .multidot.g.sup.-1 and are particularly useful for the oxidation of a feedstock with an oxygen-containing gas, e.g. catalytic combustion, especially under conditions such that the catalyst attains a temperature of at least 1000.degree. C.