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Distributed systems with multiple amplify-andforward (AF) relays are very appealing, due to their ease of implementing space diversity. Although their performance on synchronous flat-fading channels was well understood, the corresponding design and optimization in asynchronous frequency selective fading (AFSF) channels remains unsolved. In this paper, we tackle the problem in the information-theoretic framework, revealing that multi-relay amplify-and-forward (MR-AF) systems over AFSF channels can be better understood through the concept of virtual sub-channels. Each relay node virtually performs two functions, appropriately amplifying sub-channel signals on one hand and serving as a local switching center on the other. System design, therefore, reduces to the determination of optimal amplification factors, switching matrices, and power allocation among the source, relays and relevant sub-channels. The optimization is implemented in a layered structure. The effects of asynchronism and knowledge of channel information on mutual information are also investigated.