In a brief history of parapsychology the meaning of the term ESP, some of the evidence for its existence and its importance to psychology are discussed. The traditional view, that ESP is a form of perception is seen to be untenable and an alternative, that it is more like memory, is considered. Memory theories of ESP, and the evidence linking the two processes are discussed and a programme of research to test these models of ESP outlined. The first part of the research included 3 types of experiment. (1) investigating the types of errors or confusions made in ESP (2) varying the kind of target material used, and (3) testing correlations between ESP and memory ability. In none of these experiments was evidence of ESP obtained. It was therefore impossible to test specific hypotheses about the nature of ESP. Further analyses failed to detect position or variance effects in the data and no relationship to certain subject variables was found. Further experiments were designed to eliminate possible weaknesses in the previous ones and to explore different methods for eliciting ESP. Young children were used as subjects, subjects were trained in relaxation and imagery, tested for ESP in the ganzfeld and three experiments investigated the Tarot. None of these methods successfully improved ESP scoring. It was concluded that the chance hypothesis best accounted for the data obtained. Two possibilities were discussed (1) that ESP does occur in certain circumstances but did not occur here because of adverse conditions, subjects, experimenter or whatever. (2) that ESP does not ever occur and the results of experiments claiming to provide evidence for ESP have to be explained some other way. The implications of each view, and the research to which each might lead are considered.