When several ability scales in item response models are separately derived from different test forms administered to different samples of examinees, these scales must be equated to a common scale because their units and origins are arbitrarily determined and generally different from scale to scale. A general method for equating logistic ability scales was developed that uses a least squares method with weights reflecting the relative importance of correct equating at the various values on the ability continuum. The method is characterized by explicit definition of the equating error on the probability scale, minimization of the overall error, and coherence of the equating in all directions. It is applicable when the test forms are linked by common items, and various linkage patterns can be used. When there are more than m - 1 links among m test forms, a restricted solution is provided to insure an internally consistent system of equatings. Results of the application of the method to many computer-generated data sets indicated that the accuracy of the obtained estimates of the equating constants was generally satisfactory and that the number of common items in the linked pairs of test forms was the most important factor in determining the accuracy of estimation. (Author/GK)