This paper presents a diagnostic methodology relying on a set-membership approach for fault detection and on a causal model for fault isolation. Set-membership methods are a promising approach to fault detection because they take into account a priori knowledge of model uncertainties and measurement errors. Every uncertain model parameter and/or measurement is represented by a bounded variable. In this paper, detection consists of verifying the membership of measurements to an interval. First order discrete time models are used and their output is explicitly computed with interval arithmetic. Fault isolation relies on a causal analysis and the exoneration principle, which allows focusing the consistency tests on simple local models. The isolation strategy consists of two steps: performing minimal tests found with the causal graph and determining on line additional relevant tests that reduce the final diagnosis. An application for a nuclear process is used in order to illustrate the method's efficiency. (C) 2004 Published by Elsevier Ltd.