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Most of grid applications require a large amount of memory resources. If there is not enough memory supplied during execution, the program performance will be significantly degraded by page swapping. To address this problem, we propose a remote paging system called Grid Remote Pager (GRP) for grid computing in this paper. Compared with other remote paging systems, GRP keeps high portability and transparency. The more important matter is that it actively adapts the limit of the amount of memory available for user programs according to the memory load of owner jobs. Consequently, not only the competition of memory between owner programs and user programs is effectively alleviated but also sufficient exploitation of free memory is achieved by user programs with the support of GRP.