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The presented work is part of our long-term research goal to develop parallel SAT solving methods for large scale Peer-to-Peer Desktop Grids, which aggregate globally distributed resources. In such a parallel environment, appropriate strategies for dealing with massive parallelism are necessary. In particular, efficiency and at the same time robustness of the parallel methods must be ensured. In this paper, we report on a hybrid strategy for parallel SAT Solving, which combines exploratory and competition parallelism in an adaptive way to meet these goals.