Middleware for ubiquitous computing are having a mediator role in ubiquitous systems. They have to be able to handle both dynamics: the dynamic of the environment and of the application. But, at least, they must consider the dy- namic of the underlying software infrastructure. To handle such a dynamic, we present in this paper a mechanism for adaptation called cascaded aspects of assembly (AA). The functional decomposition proposed by cascaded AAs allows to dynamically compose adaptations to manage the dynamic variability of the application and of its infrastructure. Because cascaded AA can be selected/unselected or edited at runtime, some others processes can manage them in various autonomous and decentralized processes to handle the other dynamics.