The main contribution of this paper is twofold. First, we present an appropriate schedulability analysis, based on response time analysis, for supporting fault-tolerant hard real-time systems. We consider systems that make use of error-recovery techniques to carry out fault tolerance. Second, we propose a new priority assignment algorithm which can be used, together with the schedulability analysis, to improve system fault resilience. These achievements come from the observation that traditional priority assignment policies may no longer be appropriate when faults are being considered. The proposed schedulability analysis takes into account the fact that the recoveries of tasks may be executed at higher priority levels. This characteristic is very important since, after an error, a task certainly has a shorter period of time to meet its deadline. The proposed priority assignment algorithm, which uses some properties of the analysis, is very efficient. We show that the method used to find out an appropriate priority assignment reduces the search space from O(n!) to O(n/sup 2/), where n is the number of task recovery procedures. Also, we show that the priority assignment algorithm is optimal in the sense that the fault resilience of task sets is maximized as for the proposed analysis. The effectiveness of the proposed approach is evaluated by simulation.