An analysis of the skills necessary for performance on the Test of English as a Foreign Language (TOEFL) tends to support the view that there are important, although subtle, secondary dimensions present in the test. This research explored the feasibility of an item response theory (IRT) based method of modeling examinee performance on these secondary ability dimensions. Both exploratory multidimensional IRT (MIRT) and confirmatory multidimensional IRT (CMIRT) models were investigated in the study. The work performed included the application of unidimensional IRT, MIRT, and CMIRT models in two TOEFL forms to evaluate the extent to which model fit is enhanced by using a multidimensional model and to determine to what extent the additional fitted ability dimensions correspond to meaningful cognitive processes or content areas. Results indicate that the MIRT and CMIRT procedures were successful in modeling secondary ability dimensions on TOEFL and that they provide corroborative evidence in interpreting the structure of the test that is consistent with previous structure interpretations. The data also illustrate how the consistent Akaike information criterion can identify the best competing models of test structure. Four figures (plots) and seven tables illustrate the discussion. (Contains 34 references.) (SLD)