This paper compares the efficiency and plausibility of published computational models of familiarity discrimination in the perirhinal cortex. Much evidence indicates that the perirhinal cortex is involved in both the familiarity discrimination aspect of recognition memory and in perceptual functions to do with representations of complete stimuli (object identification). Published models of how the perirhinal cortex may perform familiarity discrimination can be divided into two groups. The first group assumes that a proportion of perirhinal neurons form a network specialised just for familiarity discrimination (these models may be based on Hebbian or anti-Hebbian synaptic plasticity). In contrast, the second group assumes that both familiarity discrimination and learning representations of complete stimuli are performed within a single combined network. This paper establishes that when the responses of neurons providing input to the familiarity discrimination network are correlated (as is indicated by experimental data), then specialised networks based on anti-Hebbian learning may recognise the previous occurrence of many more stimuli (have a capacity up to thousands of times larger) than specialised networks based on Hebbian learning. The currently published combined models do not learn an optimal stimulus representation (they do not fully extract statistically independent features), and hence their capacities are even lower than those of the specialised models based on Hebbian learning. Hence, the combined models as so far published are critically less efficient than the specialised models based on anti-Hebbian learning. The paper also compares the consistency of the models with experimental observations concerning what is known of synaptic plasticity in the perirhinal cortex and the responses of its neurons. Many theoretically important parameters remain undetermined and suggestions are made of experiments to provide information critical for refining and distinguishing between the various models. However, the above theoretical arguments and currently published data favour the existence of a separate network specialised for familiarity discrimination.