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Multi-level methods use a hierarchy of successively finer grids. In an adaptive unstructured grid hierarchy each grid is obtained by solution-dependent refinement of the grid on the previous level. In this paper the load balancing issues involved in the parallel implementation of an unstructured multi-grid algorithm with run-time grid refinement for the steady Euler equations on a distributed memory computer are discussed. A number of techniques for data partitioning and mapping are proposed. The parallel performance of the code is evaluated on hypercube computers.