Unidimensional item response theory (IRT) is widely used in the analysis and equating of educational achievement tests. If an IRT model is true, item response must be locally independent when the trait is held constant. Several measures of local dependence which are used in conjunction with the three-parameter logistic model in the analysis of mathematics achievement tests at each of grades 3 and 6 are presented. Measures of local dependence were useful for identifying subsets of items that were influenced by the same factors (simulated data) or that had similar content (real data). Item pairs with high local dependence values tended to have similar item parameters, but most items with similar item parameters did not have high local dependence values. Sets of locally dependent items were difficult and discriminating if the items involved an accumulation of the skills involved in the easier items in the rest of the test; locally dependent items which were independent of the other items in the test did not have unusually high or low difficulties or discriminations. Substantial systematic errors of equating were only found when the two tests measured quite different dimensions that were presumably taught sequentially. (Author/DWH)