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With the increasing popularity of network applications, mobile codes become a promising technology to provide scalable services. Due to their mobile nature, it is a challenge to support synchronous transient communication between mobile objects. This work presents a reliable connection migration mechanism that allows mobile objects in communication to remain connected during their migration. This mechanism supports concurrent migration of both end-points of a connection and guarantees exactly-once delivery of all transmitted data. In addition, a mobile code access control model is integrated to ensure secure connection migration. This work presents the design of the mechanism and a reference implementation, namely NapletSocket, over Java Socket in a mobile agent system. Experimental results show that NapletSocket incurs a moderate cost in connection setup, mainly due to security checking, and marginal overhead for communication over established connections. Furthermore, we investigate the impact of agent mobility on communication performance via simulation. Simulation results show that NapletSocket is efficient for a wide range of migration and communication patterns.