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This paper proposes an asynchronousheterogeneous propagation approach of concurrent competitive waves forhyper-distributed hyper-parallel heuristic problem-solving. Thisapproach is much more powerful than the synchronous homogeneousmechanisms and the asynchronous superimposition algorithms, and hasuniversal validity and availability. The basic conception, concurrentalgorithm and its properties are discussed. The theory and conclusionsdrawn in this paper are of essential importance for the hardwareimplementation of hyper-distributed hyper-parallel processing based onchaotic cellular networks.