A symmetric algorithm is proposed for detecting distributed termination in a dynamic system with asynchronous communication networks. Correctness of the algorithm is proven. In the system, active processes may create new processes or accept outside processes to join the basic computation. No processes can be destroyed or leave the system until the computation terminates. The network model exploited in the algorithm is a combination of a logical ring and computation trees. It is more general and especially suitable for the applications on Internet networks. The algorithm is more ef.cient than those in previous works in terms of control messages used in the detection protocol.