Recently, several states have expressed interest in linking their statewide assessments to the National Assessment of Educational Progress (NAEP) in the hope that, through equating, they can be compared to national results. This study considers the degree to which existing statewide assessments may be linked to NAEP, without violating the basic assumptions of equating. Results of statewide assessments and of the NAEP Trial State Assessment (TSA) in eighth grade mathematics for both 1990 and 1992 were obtained from four states and equipercentile equating procedures were used. The equating functions for males and females in the two states providing gender identification were similar at the low end of the scale but diverged at the high end of the scale. Estimates of the 1992 NAEP scores derived from applying the 1990 equating functions to the 1992 statewide data were generally similar to actual NAEP results near the median, but were quite dissimilar in the tails of the distribution. These results suggest that such linking, while reasonable for estimating average performance for a state, is not sufficiently stable to use for making comparisons based on the tails of the distribution. (Contains 11 references, 9 tables, and 5 figures.) (Author)