The dynamism and scale of the infrastructure of the Internet of Services bring new needs to build autonomous services. These services have to be able to self-adapt to the variation of the environment. Moreover, these adaptations may span across multiple services and thus have to be coordinated, without breaking their autonomy. To this end we describe in this paper the approach we have chosen for SAFDIS, a framework to make coordinated adaptations of services. In this presentation, a particular emphasis is made on the distribution of the framework and how it helps to coordinate distributed adaptation. Benefits from the self-adaptation of the framework itself are also presented. Keywords-Dynamic Adaptation; Distributed Services; Distributed Adaptation; Self-Adaptation of Adaptation Framework.