Much evidence indicates that recognition memory involves two separable processes, recollection and familiarity discrimination, with familiarity discrimination being dependent on the perirhinal cortex of the temporal lobe. This thesis introduces and analyses new neural network models designed to mimic the response patterns of perirhinal neurons that signal information concerning the novelty or familiarity of stimuli. The models achieve very fast and accurate familiarity discrimination while employing biologically plausible parameters and learning rules. The networks determine whether a stimulus has been encountered before, but not its associations; accordingly, the models cannot be used to achieve associative recall. Given this restriction, the networks achieve much higher storage capacity for familiarity discrimination than associative memory neural networks achieve for recall. The capacity of the models establishes that the perirhinal cortex alone may discriminate the familiarity of many more stimuli than current neural network models indicate could be recalled (recollected) by all the remaining areas of the cerebral cortex. The thesis also shows how different types of perirhinal neurons can co-operate during familiarity discrimination and thus provides an explanation for the interactions between the perirhinal neurons observed in vivo. Different models of familiarity discrimination are compared in terms of their efficiency and consistency with experimental observations. Both efficiency and plausibility suggest that the operation of the perirhinal familiarity discrimination network is similar to one of the specialised models, which assumes that a proportion of the perirhinal neurons form a network specialised just for familiarity discrimination and not involved in other perceptual and memory functions of the perirhinal cortex. The efficiency and speed of detecting novelty provides an evolutionary advantage, thereby providing a reason for the existence of a familiarity discrimination network in addition to networks used for recollection.