The medical decision-making community has an extensive literature on the use of receiver operating characteristic (ROC) graphs for diagnostic testing. Heagertybiet al. have recently developed this ROC curve theory within the context of survival data (Biometrics 2000; 56:337–344). The time-dependent ROC method allows evaluating the accuracy of a marker to predict a time-dependent failure, whereas the classic methodology focuses on diagnosis. One limitation to this approach, however, is to analyse a single failure. In many medical situations, a marker can be useful to predict different competitive failures. For example in kidney transplantation, the terminal evolution can be a return to dialysis or the death of the patient. With this application in mind, our paper proposes an extension of the time-dependent ROC method for analysing the accuracy of a marker to predict two competitive events. Copyright © 2010 John Wiley & Sons, Ltd.