Abstract: The abstract concept of equivalence is considered one of the bases of higher-order cognition, and it has been the subject of considerable research in comparative cognition. This study examined the conditions under which tufted capuchin monkeys (Cebus apella) are able to acquire an identity concept. Six capuchin monkeys were trained to solve a visual matching-to-sample (MTS) task on the basis of perceptual identity. The acquisition of the identity rule was inferred from the subject’s ability to solve transfer tests with novel stimuli. We evaluated the ability of the capuchin monkeys to match the shape of novel stimuli after training with both several small stimulus sets (Experiment 1) and a large stimulus set (Experiment 2). Moreover, we examined the ability of capuchins to transfer the concept to novel visual dimensions, such as colour and size and to transfer to novel spatial arrangements of the stimuli (Experiment 2). We demonstrated that the ability of capuchins to match novel stimuli was improved by increasing the number of stimuli used during training (Experiments 1 and 2) and that after a widely applicable identity concept based on the stimulus shape was acquired, the capuchins were able to match stimuli according to an identity rule based on both the colour and size of the stimuli and when the spatial arrangement of the stimuli was varied (Experiment 2). This study is the first to demonstrate that the size of the training set affects the acquisition of an abstract identity concept in an MTS task in non-human primates.