A method for treating cooking fumes to oxidize oxidizeable particulate and gaseous components thereof includes contacting the fumes with a catalytic material containing ceria and alumina each having a BET surface of at least about 10 m.sup.2 /g, for example, ceria and activated alumina in a weight ratio of from about 1.5:1 and 1:1.5 and a BET surface area of from about 25 m.sup.2 /g to 200 m.sup.2 /g. Optionally, a catalytic metal component such as platinum or palladium may be included in the catalytic material. The foodstuffs cooking fumes are contacted with the catalyst composition (22 or 40) at a temperature of 200.degree. C. to 600.degree. C. to promote the oxidation of both particulate (atomized) animal and/or vegetable oils and fats and oxidizeable gas phase components of the fumes. Optionally, a separate, supplemental gas phase oxidation catalyst (42) may be used in conjunction with and downstream of the above-described catalyst (40) to provide a two-catalyst system for treating cooking fumes.