The Unified Modeling Language (UML) has become the standard language for the design of object-oriented software systems over the past decade. Even though there exist various tools which claim to support design with UML, their functionality is usually focused on drawing UML diagrams and generating code from the UML model. The task of choosing a suitable design which fulfils the requirements still has to be accomplished by the human designer alone. The aim of this thesis is to develop concepts for UML design tools which assist the modeller in improving the system design and requirements incrementally. For this approach a variant of formal games called exploration games is introduced as underlying technique. Exploration games can be defined on the basis of incomplete and imprecise UML models as they occur frequently in practice. The designer repeatedly plays an exploration game to detect flaws or incompleteness in the design and its specification, which are both incorporated in the game definition. At any time the game definition can be incremented by the modeller which allows him to react to the discoveries made during a play and experiment with new design solutions. Exploration games can be applied to UML in different variants. For each variant must be specified how the UML diagrams are used to set up the game and how the semantic variation points of UML should be interpreted. Furthermore some parts of the game definition may not be contained in the UML model and have to be provided separately. The emphasis of this thesis is on game variants which make use of UML diagrams for modelling system behaviour, especially state machines and activity diagrams. A prototypical implementation demonstrates how the concepts developed in this thesis can be put into practice. The tool supports the user in defining, playing and incrementing a game. Moreover it can compute winning strategies for the players and may act as opponent of the modeller. As example a game variant based on UML state machines has been implemented. The architecture that has been chosen for the tool leaves room for extension by additional game variants and alternative algorithms.