Software components are now widely used in the development of systems. However, incompatibilities between their behavioural interfaces may make their composition impossible. The objective of software adaptation is to compensate such incompatibilities building as automatically as possible corrective connectors or components. Constructing component-based systems from scratch is difficult, in particular when components cannot be used directly since they have to be adjusted with respect to their mates. Incremental construction methods are therefore essential because they make it possible to build systems step by step and therefore to master the complexity of their adaptation. In this paper, we propose an incremental approach to build component-based systems which relies on the generation of adaptors to overcome behavioural incompatibilities. The adaptation stage can be automated being given act mapping formalising the properties of the system to be adapted. Key words: Software Components,...