Summary To develop more targeted intervention strategies, an important research goal is to identify markers predictive of clinical events. A crucial step toward this goal is to characterize the clinical performance of a marker for predicting different types of events. In this article, we present statistical methods for evaluating the performance of a prognostic marker in predicting multiple competing events. To capture the potential time-varying predictive performance of the marker and incorporate competing risks, we define time- and cause-specific accuracy summaries by stratifying cases based on causes of failure. Such definition would allow one to evaluate the predictive accuracy of a marker for each type of event and compare its predictiveness across event types. Extending the nonparametric crude cause-specific receiver operating characteristics curve estimators by Saha and Heagerty (2010), we develop inference procedures for a range of cause-specific accuracy summaries. To estimate the accuracy measures and assess how covariates may affect the accuracy of a marker under the competing risk setting, we consider two forms of semiparametric models through the cause-specific hazard framework. These approaches enable a flexible modeling of the relationships between the marker and failure times for each cause, while efficiently accommodating additional covariates. We investigate the asymptotic property of the proposed accuracy estimators and demonstrate the finite sample performance of these estimators through simulation studies. The proposed procedures are illustrated with data from a prostate cancer prognostic study.