Ubiquitous computing environments are becoming more heterogeneous and highly dynamic. Systems need to dynamically self-adapt in order to accommodate dynamically changing resources, needs of different users and failure events. This paper focuses on the runtime adaptation mechanisms that need to be dealt with the distributed nature of systems and the heterogeneity of the environment. We tackle the problem of distributed management of dynamic adaptation where separate adaptation processes are performed concurrently. We elaborate mechanisms to coordinate adaptation processes in order to improve the correctness of the system during and after the adaptation. We implement a framework that offers the required support for distributed management of adaptability. The framework is customizable to meet application-specific requirements and the operating environment characteristics. Our focus will be on the architectural principles and the coordination mechanisms of the framework. We developed a self-adaptive replication system based on our framework for the specification and the enforcement of the adaptation mechanisms.