With the increased adoption of technologies like wireless sensor networks by real-world applications, dynamic network topologies are becoming the rule rather than the exception. Node mobility, however, introduces a range of problems (communication interference, path uncertainty, low quality of service and information loss, etc.) that are not handled well by periodically refreshing state information, as algorithms designed for static networks typically do. To address specifically this problem, the main contribution of this paper is the introduction of a novel mechanism (called ASH) for the creation of a quasi-static overlay on top of a mobile topology. It is powered by simple, local interactions between nodes and exhibits self-healing and self-organization capabilities with respect to failures and node mobility. We show that the overlay mechanism works without assumptions about position, orientation, speed, motion correlation, and trajectory prediction of the nodes. A preliminary evaluation by means of simulation shows that ASH succeeds in tackling node mobility, while consuming only minimal resources.