Four patients with ‘developmental dyscalculia’ are described who were initially identified on the basis of clinical tests, reports of longstanding and severe difficulties in arithmetic, and psychological test results. Descriptive psychological testing indicated (1) that the arithmetical deficits could not be accounted for on the basis of a generally low level of intellectual functioning; (2) that of the four basic arithmetical processes that of multiplication was relatively more deficient; (3) that this relative deficiency in multiplication stemmed from a faulty grasp of basic multiplication tables; that this was a real difficulty, experienced subjectively by the patient, and one that could not be accounted for simply by carelessness; and finally, that the degree of difficulty experienced varied with the multiplication table involved. Two kinds of attempt were made to improve arithmetical functioning. The first involved brief remedial coaching programmes directed at the basic multiplication tables: relatively little success was obtained with this method. The second kind of attempt involved methods of bypassing the necessity for learning multiplication tables: some success was obtained with these methods. The discussion concentrates on some of the features which may provide possibly useful cues for identifying ‘developmental dyscalculia’: these are classified in terms of: (1) pattern of deficit displayed; (2) qualitative features of arithmetical performance; and (3) response to remedial teaching. Some suggestions are made concerning further lines of investigation.