Redundancy is necessary for fault tolerance, but the overhead introduced by redundancy may degrade system' performance. In this paper, we propose efficient replication-based algorithms for fault-tolerant mobile agent execution, which enable parallel processing in the agent execution to reduce the overhead caused by redundancy. We also investigate failure detection mechanisms and identify the problems of the heartbeat style failure detection approach and modify it for use in our proposed algorithms. Performance evaluation has been performed to compare the proposed algorithms with the existing algorithm. Both analytic and simulation results show that our new algorithms can significantly improve the system performance.