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A numerical method is developed for the simulation of rotor stator interactions in a compessor or turbine stage. This method solves quasi three dimensional Navier Stokes equations by an implicit high resolution finite volume approach. A fully conservative method is designed to compute the inviscid and viscous fluxes at the interface of rotor and stator grids. Numerical results of rotor stator interactions in a transonic compressor stage are presented. The mechanism of rotor stator interactions in this compressor stage is discussed in terms of the computational results.