This work is concerned with the problem of constructing associative memory models which store and retrieve information in a distributed fashion - that is each store location can be involved in the storage of more than one piece of information. The models are to be logically simple in form and efficient in their use of store. It is hoped that those proposed may find a place in neurophysiological theories of memory. From the starting point of seeking a less complex representation of a holographic model of memory called the Holophone, several memory models have been proposed and their properties investigated by analytical and computer simulation methods. All the systems considered belong to a family of memory models which are described by a pair of matrix equations. It is found that the models which perform well are non-linear devices which have to store and retrieve highly redundant information. One of these, the Associative Net, is closely related to a recent theory of the cerebellum. Some of the contents of Chapters 3, 4 and 5 have already appeared in papers published in collaboration with H.C. Longuet-Higgins and O.P. Buneman. Otherwise this dissertation is believed to be original in content and in arrangement.