Three methods for the estimation of the reliability of single dichotomous items are discussed. All methods are based on the assumptions of nondecreasing and nonintersecting item response functions and the Mokken model of double monotonicity. Based on analytical and Monte Carlo studies, it is concluded that one method is superior to the other two because it has a smaller bias and a smaller sampling variance. Furthermore, this method shows some robustness under violation of the condition of nonintersecting item response functions. Item reliability is of special interest for Mokken's nonparametric item response theory and is useful for the evaluation of item quality in nonparametric test construction research. It is also of interest for nonparametric person fit analysis. (Contains 1 figure, 2 tables, and 33 references.) (Author/SLD)