The equating of reasonably parallel forms of College Board Achievement Tests in biology, chemistry, mathematics level II, American history and social studies, and French is discussed. Results of the following five equating methods are compared: (1) Tucker; (2) Levine equally reliable; (3) Levine unequally reliable; (4) frequency estimation equipercentile; and (5) chained equipercentile. These methods are used with an internal common-item anchor-test data collection design and three sampling strategies (random samples from populations similar in ability level, random samples from populations of dissimilar ability, and samples from dissimilar populations constructed to be similar by matching on the basis of a covariate such as the distribution of scores on a set of common items). Results indicate that it may be difficult, and in some cases impossible, to equate achievement tests using new-form and old-form samples from populations differing in ability level. All these equating methods appear to be affected by group differences in ability, with the Tucker and frequency estimation equipercentile methods the most affected, and the chained equipercentile and the two Levine procedures the most robust. Matching cannot be recommended for rectifying sample ability-level differences. There are 17 tables of study data, 33 figures, and a list of 16 references. (Author/SLD)