Recently, L. Zeng and M. J. Kolen (1995) have introduced item response theory (IRT) observed score (OS) equating of number-correct (NC) scores for equating different forms of a test. In this paper, IRT-OS-NC equating is adapted to equating the cut-off scores of examinations. Next, the differences between results obtained using a Rasch model for polytomously scored items and results obtained via the nominal response model are evaluated. For both versions of IRT-OS-NC equating confidence intervals are derived. Finally, two procedures for testing the validity of the procedure are presented. Differences between the two versions were not very large. The methods studied here are exemplified with the results of equating a number of the examinations in secondary education in the Netherlands. Some limitations of the approach are discussed. (Contains one figure and seven tables.) (Author/SLD)