The aggregation hierarchy is one of the most significant data abstraction mechanisms that emerged as a result to semantic extensions to traditional systems analysis and design methods. The way inheritance works in this hierarchy is studied in this thesis. Special emphasis is placed on the behaviour of objects which are related via an aggregation hierarchy. A framework is introduced for capturing the behaviour of a system from the respective behaviour(s) of its components. This framework is based on a 3-level behaviour modelling hierarchy. One of the most significant contributions of this framework is the ability to apply inter-object interactions when building a behaviour model of a system. These interactions are significant in that they can yield totally distinct models of the systems functionality. Some of the notions that are supported by the behaviour modelling framework include unreachable and transient states, transition chains (cascades) and concurrency. The framework also enables the creation of behaviour model (semantic) hierarchies, wherein certain facets of the systems behaviour or functionality can be hidden (abstracted out) in a gradual fashion that suits the requirements of the problem domain. This creates what is effectively, distinct views of the behaviour or functionality of the system. The notions and concepts that are introduced here are verified and presented in a comprehensive case study that shows what can be achieved using these ideas. Suggestions are also made for future work which can help overcome some of the limitations introduced throughout this research.