A process for feeding a companion animal such as a dog a diet containing an effective amount of a combination of antioxidants to enhance immune response and improve the overall health of the animal is provided. Preferably, the diet includes from about 175 to about 400 IU of vitamin E per kilogram of diet, from about 1 to about 50 mg/day of lutein, and from about 1 to about 50 mg/day of beta-carotene.