These experiments examined the behaviour of brushtail possums (Trichosurus vulpecula) under concurrent variable-interval schedules of reinforcement. In the first experiment the lever pressing of six possums resulted in intermittent access to a barley/carob mixture under four pairs of variable-interval schedules. In most respects, the behaviour of the possums was similar to that observed with other species. However, the degree of undermatching of the response ratios to the obtained reinforcement-rate ratios was greater than is normally observed with these schedules. Both the Generalised Matching Law and the Contingency-Discriminability model described the data well, although, where overmatching was obtained, the parameter values given by the Contingency-Discriminability model did not make sense in terms of the original assumptions of the model. The second experiment examined the possibility that the undermatching related to the length of the changeover delay used. Six possums were exposed to five different pairs of concurrent schedules at each of four different changeover-delay lengths (ranging from 0 to 6 s). Time allocation and post-changeover delay responses more closely approximated matching with a 2-s changeover delay than with a 0-s delay, but no further changes in sensitivity were observed with further increases in changeover-delay length. Overmatching was consistently observed in the post changeover delay data, resulting in un-interpretable parameter values from Contingency-Discriminability analyses. The addition of the punishment parameter (w) to the Contingency-Discriminability model, suggested to deal with such data, did not generally result in more sensible parameter estimates. The third experiment attempted to bias possums responding using qualitatively different reinforcers. Equal variable-interval schedules were used with the barley/carob mixture available on one schedule and Cocopopsᵀᴹ or coconut on the other. Possums’ behaviour was biased by these foods, with a small bias away from the barley/carob mixture resulting from the Cocopops and a large bias towards the barley/carob mixture resulting from the coconut. In the fourth experiment, graded point estimates of bias were obtained by presenting four different concentrations of salted barley/carob mixture (ranging from 0% to 6%) on one schedule and plain barley/carob mixture on the other schedule. Small biases were found with 0% and 2% salt, and large biases were found towards the barley/carob mixture with 4% and 6% salt. To assess whether bias remains constant with changes in the reinforcer-rate ratio, further conditions were conducted with 4% and 6% salt, with four pairs of unequal concurrent variable-interval schedules. Analyses of these data with both the Generalised Matching Law and the Contingency-Discriminability Model revealed an interaction between bias and the reinforcement-rate ratio. This interaction may be due to an improvement in discriminability due to the different reinforcers. The behaviour of the possums was generally well described by both the Generalised Matching Law and the Contingency-Discriminability model. Overall, neither model was better at describing behaviour under the above conditions, although several problems were found with the application of the Contingency-Discriminability model.