The modeling of behavior in object-oriented systems usually relies on control flow diagrams and (extended) state automatas. These basic techniques do not well support the design in a declarative style. This style is useful for modeling integrity constraints, especially active constraints, on the data model, to perform event handling, to derive new attribute values and associations, and to model strategies in business and engineering. In this contribution, rules are added as a declarative modeling technique for behavior. Roughly speaking, a rule consists of a condition and an action. If the condition is true, the action is performed. The concept of rules is integrated into an existing object-oriented modeling technique by formulating rules on object diagrams. A rule application may test and change a certain object structure. The application may be triggered automatically by a relevant change of this object structure, periodically or by an event occuring in some behavior diagram. This rule concept has an underlying formal semantics on the basis of graph transformation which may be exploited for analyzing a designed rule set concerning e.g. conflicts, dependencies, etc. The graphical notation of the rules follows the UML-notation as far as possible.