In this paper, we study robust failure diagnosis of discrete event systems. Given a set of possible models, each of which has its own nonfailure specification, we consider the existence of a single diagnoser such that, for all possible models, it detects any occurrence of a failure within a uniformly bounded number of steps. We call such a diagnoser a robust diagnoser. We introduce a notion of robust diagnosability, and prove that it serves as a necessary and sufficient condition for the existence of a robust diagnoser. We then present an algorithm for verifying the robust diagnosability condition. (C) 2012 Elsevier Ltd. All rights reserved.