Behavioural plasticity allows animals to adjust rapidly to local environmental conditions, but at the risk of erroneously changing behaviour in response to irrelevant events. Adaptive biases or predispositions constrain learning and reduce such potential costs. Preferential learning about complex biologically-meaningful stimuli, such as predators, has been investigated in only a few systems and there have been no experimental tests for the presence of adaptive biases in a marsupial. We have previously shown that tammar wallabies (Macropus eugenii) became fearful of a model fox (Vulpes vulpes) after it was repeatedly paired with an aversive event. Tammars generalized their acquired response to a cat (Felis catus), but not to a non-predator (juvenile goat, Capra hircus), suggesting that they might have a bias to associate predators with frightening events. The present study tested this idea directly. We used an experimental design identical to that of earlier predator-training experiments, but substituted a model goat for the fox as the stimulus predicting a capture attempt. A control group had the same total experience of the goat and of a human with a net, but without any predictive relationship between these two events. We detected no change in behaviour towards the goat, or to any of an array of control stimuli, as a consequence of training. This finding contrasts strongly with the effects of the same pairing procedure using a fox model. Taken together, these studies provide the first evidence for an adaptive predisposition to acquire a fear of predators in marsupials. Learning processes in this group are thus evolutionarily convergent with those previously described in eutherian mammals.