The theory, purpose and methods of LOGIST, a computer program for estimating examinee ability and item characteristic curve parameters, is described. Minimum input required is the number of items, number of examinees, number of alternative choices per item and the responses of each examinee to each item (00 if wrong, 01 if correct, 10 if omitted and 11 if not reached). Final output contains the estimated item parameters and abilities, printed and punched. After the initial run the program prints the proportion of correct responses for each item and the Kuder-Richardson reliability co-efficient KR20 and KR21, plus the number of examinees that omitted each item and the number that reached each item. The intermediate printout contains sufficient information for following the progress of the iterations. For each item there are three parameters, the discriminating power, the difficulty and the lower asymptote of the item characteristic curve, and there is one ability parameter for each examinee. Thus, there are N+3n parameters to be estimated, where N is the number of examinees and n is the number of items. A lengthy iterative procedure for dealing with such a large number of parameters is described in detail. It requires repetition of stages until the procedure converges. Rules and restrictions for achieving convergence and two methods of speeding the procedure are described. Input options are described in detail in the appendix.