We study inference methods for the analysis of multireader diagnostic trials. In these studies, data are usually collected in terms of a factorial design involving the factors Modality and Reader. Furthermore, repeated measures appear in a natural way since the same patient is observed under different modalities by several readers and the repeated measures may have a quite involved dependency structure. The hypotheses are formulated in terms of the areas under the ROC curves. Currently, only global testing procedures exist for the analysis of such data. We derive rank‐based multiple contrast test procedures and simultaneous confidence intervals which take the correlation between the test statistics into account. The procedures allow for testing arbitrary multiple hypotheses. Extensive simulation studies show that the new approaches control the nominal type 1 error rate very satisfactorily. A real data set illustrates the application of the proposed methods.