In this paper we show by using the example of UML, how a software engineering method can benefit from an integrative mathematical foundation. The mathematical foundation is given by a mathematical system model. This model provides the basis both for integrating the various description techniques of UML and for implementing methodical support. After describing the basic concepts of the system model, we give a short overview of the UML description techniques. Then we show how they fit into the system model framework and sketch an approach to structure the UML development process such that it provides methodological guidance for developers.