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Web service may be used to construct autonomic business processes, where several Web services interact with each other to carry out complex transactions or workflows. During the execution of an autonomic process, if one component service fails or becomes overloaded, a mechanism is needed to ensure that the running process is not interrupted and the failed service is quickly and efficiently replaced. In this paper, we present two algorithms to solve the problem. The first algorithm uses the backup path approach so that the predecessor of a failed service may quickly switch to a predefined backup path. The second algorithm uses the replacement path approach to re-construct a new process by skipping a failed service. All these dynamic adaptations can be done by business process itself or a QoS broker which is part of an autonomic system. The simulation result shows that, when producing the information needed for dynamic adaptation, the running time of business process composition increases only by a constant factor regardless of the system size.