Object-oriented analysis and design is an increasingly popular software development method. The Unified Modeling\ud Language (UML) has recently been proposed as a standard language for expressing object-oriented designs. Unfortunately, in its present form the UML lacks precisely defined semantics. This means that it is difficult to determine whether a design is consistent, whether a design modification is correct and whether a program correctly implements a design.\ud Formal methods provide the rigor which is lacking in object-oriented design notations. This provision is often\ud at the expense of clarity of exposition for the non-expert. Formal methods aim to use mathematical techniques in\ud order to allow software development activities to be precisely defined, checked and ultimately automated. This paper aims to present an overview of work being undertaken to provide (a sub-set of) the UML with formal semantics. The\ud semantics will facilitate the use of the UML in the software development process by allowing development steps to be defined and checked.