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Summary form only given. We describe the parallelization of the multizone code versions of the NAS parallel benchmarks employing multilevel OpenMP parallelism. For our study we use the NanosCompiler, which supports nesting of OpenMP directives and provides clauses to control the grouping of threads, load balancing, and synchronization. We report the benchmark results, compare the timings with those of different hybrid parallelization paradigms and discuss OpenMP implementation issues which effect the performance of multilevel parallel applications.