Abstract. We investigate how a formalism known as a basis and common to many areas of applied mathematics and engineering can be applied to perfective maintenance and the integration of application systems in software engineering, using an object-oriented approach. It is concluded that this formalism serves as a mathematical model for perfective software maintenance and software systems integration activities under object-oriented development. Theorems and properties about the model are reported as guides to software maintenance. The model and formal maintenance techniques have been applied to a software system in the management information systems area to demonstrate this approach to perfective maintenance and to assist in validating the model.