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The basic computing models are evolving towards stronger expressiveness and higher naturalness. In grid, the focus of computation is turning from individual entities to dynamic coordination across them. Accordingly, future grid computing would be based on cooperation. This research proposes a novel model of computation namely cooperative Turing machine (CTM) for grid. It extends classical Turing machine (TM) by introducing a teamwork tape, which is shared by all participants within a team, so as to achieve cooperation during computation. Its co-inductive recursive function and behavioral streams language are defined, and new features are discussed. Finally we show the benefits from CTMs as for grid.