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We present an agent-based computational grid (ACG), which applies the concept of computational grid to agents. The ACG system is to implement a uniform higher-level management of the computing resources and services on the grid, and provide users with a consistent and transparent interface for accessing such services. All entities in the grid environment including computing resources and services can be represented as agents. Each entity is registered with a grid service manager. An ACG grid service can be a service agent that provides the actual grid service to the other grid member. Grid members communicate with each other by communication space that is an implementation of tuple space. The design and implementation of four grid protocols for grid service discovery are given. Finally, some conclusions are given.