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The suitability of coarse-grid correction operators for multigrid solution of discretized nonelliptic partial differential equations is studied. It is found that the requirements for the orders of intergrid transfers and the order of approximation of the coarse-grid operators differ in an important way from the well-known "rules" pertaining to elliptic operators. Both Galerkin coarsening and coarsening schemes based on the differential operator are examined, and new coarse-grid correction strategies are suggested in light of this analysis.