A multiobjective generalization of the heuristic search algorithm A* is presented, called MOA*. The research is motivated by the observation that most real-world problems involve multiple, conflicting, and noncommensurate objectives. MOA* explicitly accommodates this observation by identifying the set of all nondominated paths from a specified start node to a given set of goal nodes in an OR graph. It is shown that MOA* is complete and, when used with a suitably defined set of admissible heuristic functions, admissible. Several results concerning the comparison of versions of MOA* directed by different sets of heuristic functions are provided. The implications of using a monotone or consistent set of heuristic functions in MOA* are discussed. Two simple examples are used to illustrate the behavior of the algorithm.