Equating tests from different calibrations under item response theory (IRT) requires calculation of the slope and intercept of the appropriate linear transformation. Two methods have been proposed recently for equating graded response items under IRT, a test characteristic curve method and a minimum chi-square method. These two methods are compared with three mean and sigma methods using computer simulations. Ten- and 30-item tests were simulated for 300 and 1,000 examinees. Results under these simulated conditions indicate that recovery is good for all conditions. Recovery is slightly better for the long test and the large sample, but differences among all simulated conditions are quite small. Essentially no differences are observed among the linking methods. One could feel relatively comfortable using any of the five equating methods when ability and item location distributions are well-matched. The simplest equating method is the B. H. Loyd and H. D. Hoover (LH) mean and sigma method (1980). The minimum chi-square has some advantage in ease of use over the test characteristic curve method, but both are more complicated than the LH method. Eight tables present analysis results. (SLD)