Two local methods for observed-score equating are applied to the problem of equating an adaptive test to a linear test. In an empirical study, the methods were evaluated against a method based on the test characteristic function (TCF) of the linear test and traditional equipercentile equating applied to the ability estimates on the adaptive test for a population of test takers. The two local methods were generally best. Surprisingly, the TCF method performed slightly worse than the equipercentile method. Both methods showed strong bias and uniformly large inaccuracy, but the TCF method suffered from extra error due to the lower asymptote of the test characteristic function. It is argued that the worse performances of the two methods are a consequence of the fact that they use a single equating transformation for an entire population of test takers and therefore have to compromise between the individual score distributions. (Contains 4 figures.)