To date, the majority of computerized adaptive testing (CAT) systems for achievement and aptitude testing have been based on the dichotomous item response models. However, current research with polychotomous model-based CATs is yielding promising results. This study extends previous work on nominal response model-based CAT (NR CAT) and compares its ability estimation as well as its overall performance to graded response model-based CAT (GR CAT). A data set of 275 examinees was used, derived from five administrations of the College Board's Achievement Test in Mathematics, Level I, at the University of Texas, Austin. Results show that both CATs had high convergence rates despite using a small item pool and had average test lengths slightly below 16 items. The NR CAT's ability estimates were highly correlated with and not significantly different from an external criterion and showed no systematic bias in estimating ability throughout the trait continuum. In contrast, the GR CAT had a tendency to underestimate high ability examinees, although its ability estimates were highly associated with the external criterion. Educational implications of the findings include the possibility of merging computer-aided instruction and diagnostic testing with CAT. Six tables and nine graphs are included. (Author/TJH)