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This paper presents a heuristic-search algorithm called Memory-bounded Anytime Window A*(MAWA*), which is complete, anytime, and memory bounded. MAWA* uses the window-bounded anytime-search methodology of AWA* as the basic framework and combines it with the memory-bounded A* -like approach to handle restricted memory situations. Simple and efficient versions of MAWA* targeted for tree search have also been presented. Experimental results of the sliding-tile puzzle problem and the traveling-salesman problem show the significant advantages of the proposed algorithm over existing methods.