Provided are a method, system, and program for managing resources in which a local processor sends remote operation requests to be executed by a remote processor having multiple resources. In the illustrated embodiment, the local processor and the remote processor each have a resource manager, each of which maintains a control set for each resource of the remote processor. Each control set of the remote processor resource manager includes a queue for queuing remote operation requests awaiting execution in connection with the resource associated with the control set. Each control set of the local processor resource manager includes a credit counter which keeps track of permissible outstanding remote operation requests. Each local processor control set credit counter is decremented for each remote operation request for the associated resource sent to the remote processor and is incremented for each acknowledgment received from the remote processor. For each remote processor control set, the remote processor resource manager sends an acknowledgment for each remote operation request initiated in connection with the associated resource. For each local processor control set, the local processor resource manager queues remote operation requests if the control set credit counter falls below a threshold after being initialized in accordance with the capacity of the associated remote processor control set queue.