Moose ( Alces alces ) and snowshoe hare ( Lepus americanus ) appear to compete with each other. This was determined using the “natural experiments” of populations found in sympatry and allopatry on islands at Isle Royale National Park, Michigan, and manipulated exclosures. The population densities from these areas are fit to a series of competition models based upon different competitive mechanisms (Schoener 1974a), using non-linear regression techniques. A model of competition for food where the food can be separated into exclusively used and shared categories is found to predict observed densities of moose and hare best. Finally, the competition model's parameters (fraction of food shared and competition coefficients) are shown to agree with values predicted independently from a foraging model.