Oxidation catalyst compositions include a catalytic material containing ceria and alumina each having a surface area 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 to 1:1.5. Optionally, platinum may be included in the catalytic material in amounts which are sufficient to promote gas phase oxidation of CO and HC but which are limited to preclude excessive oxidation of SO.sub.2 to SO.sub.3. Alternatively, palladium in any desired amount may be included in the catalytic material. The catalyst compositions have utility as oxidation catalysts for pollution abatement of exhausts contianing unburned fuel or oil. For example, the catalyst compositions may be used in a method to treat diesel engine exhaust by contacting the hot exhaust with the catalyst composition to promote the oxidation of the volatile organic fraction component of particulates in the exhaust.