The authors present a general top-down procedure, GAO* , for searching acyclic AND/OR graphs with monotone cost functions. This procedure is a generalization of the AO* algorithm and can be viewed as a branch and bound procedure. Since monotone cost functions are very general, GAO* is applicable to a very large number of problems. For example, GAO* can be used to find the minimax value of a game tree. Furthermore, many existing game tree search procedures can be considered as special cases or slight variations of GAO* . The proof of correctness of GAO* is quite simple, which simplifies the correctness proof of AO* .