The aim of this study was to compare the demand by possums for foods under different arrangements of concurrent progressive-ratio and fixed-ratio schedules of reinforcement. In Experiment 1, every possible food pair made up of berries, chicken, egg, foliage, insects, and mushroom was presented (30 pairs in total). The requirement on the progressive-ratio schedule increased within a session and the fixed-ratio was kept constant at 30. In Experiment 2, a subset of the foods from Experiment 1 were used (chicken, mushroom, egg, and berries) and in separate conditions the fixed-ratio was either 30 or 10 responses. In Experiment 3, the foods were the same as used in Experiment 2 and the progressive-ratio schedule increased every five sessions and the fixed-ratio was kept constant at 30. Exponential models of demand were applied to consumption rates to compare the parameters of initial demand, essential value and Pmax, and break point and cross point across foods. The models described the data well and consumption rates were similar when the incrementing schedules increased within- and across sessions. Demand was highest for berries, egg, and locust in Experiment 1 and egg and chicken in Experiments 2 and 3. This finding has practical implications for understanding possum food preferences in the wild as a function of other available food sources and for informing pest control strategies of potential lures.