In this paper we address a resource sharing problem that arises in distributed systems. The problem is to provide a mechanism whereby a node can obtain, in a distributed network, control of a set of resources that are necessary in performing a certain task. The mechanism has to provide a "reasonable guarantee" that if sufficient resources are available, the node will be able to obtain them. We define what such a "reasonable guarantee" means in a dynamic environment with resources constantly being added or removed from the pool of available resources. We then propose a distributed algorithm and show that it provides such a guarantee. Finally, we suggest extensions to the basic mechanism to improve performance.