The matching law states that the strength of a response is directly proportional to its relative reinforcement. The preponderance of data supports the matching law approximately. The proposed research, to be conducted on pigeons and rats, focuses on the relation between matching and reinforcement maximization, on the interactions between matching and contingencies of reinforcement, on delay of reinforcement as a variable within the framework of the matching law, and on the dynamic processes that give rise to matching in asymptotic behavior. The long-range goal of the research is the quantification of the Law of Effect.