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Due to the shortages of static grid service in grid computing, a new paradigm of grid service (for brief, GS) - grid mobile service (GMS) is proposed and deeply studied in our lab. GMS provides a series of standard interfaces and conforms to OGSA's conventions to provide the intelligent mobile code service. Based on intelligent mobile software agent and grid technologies, GMS is the extension of grid service' type. Mobile agents wander in grid to discover, call and interact with all kinds of grid services automatically, accomplishing assigned task and providing certain services for users. GMS moves "computation" to "data", and its introduction can greatly increase grid service flexibility and validity, offering more selections and technological support to such applications as data-intensive computation, mobile computing and e-commerce etc. The purpose of this paper is to present mobile grid service's formal definition and description. The agent's lifetime and state evolvement in GMS are also discussed. Moreover, GMS hierarchy structure and communication process with GS or between GMS are presented.