After a survey of the specific features of ubiquitous computing applications and corresponding middleware requirements, we list the various paradigms used in the main middlewares for ubiquitous computing in the literature. We underline the lack of works introducing the use of the concept of Aspects in middleware dedicated to ubiquitous computing, in spite of them being used for middleware improvement in other domains. Then, we introduce our WComp middleware model, which federates three main paradigms: event-based Web services, a lightweight component-based approach to design dynamic composite services, and an adaptation approach using the original concept called Aspect of Assembly. These paradigms lead to two ways to dynamically design ubiquitous computing applications. The first implements a classical component-based compositional approach to design higher-level composite Web Services and then allow to increment the graph of cooperating services for the applications. This approach is well suited to design the applications in a known, common, and usual context. The second way uses a compositional approach for adaptation using Aspect of Assembly, particularly well-suited to tune a set of composite services in reaction to a particular variation of the context or changing preferences of the users. Having detailed Aspect of Assembly concept, we finally comment on results indicating the expressiveness and the performance of such an approach, showing empirically that principles of aspects and program integration can be used to facilitate the design of adaptive applications.