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Despite the popularity of (graphical) notations for the specification of object behaviour, there is no common understanding of what exactly constitutes the life cycle of an object. Consequently, different frameworks for the object-oriented modeling of systems allow for the specification of different kinds of behaviour. Unfortunately, the semantics of languages used in this area is often not clearly stated. In addition to the problems arising from this lack of formality, inheritance of behaviour is usually not covered by commonly used object-oriented languages. Therefore, flawless systems are difficult to build, because unpleasant surprises most easily occur if an object of a subclass is used in the context of its superclass. In the light of these problems this article states requirements for languages in the area of modeling and inheritance of object behaviour, surveys existing proposals, and introduces a novel approach.