A method and apparatus for performing fair-share preemption in a distributed computing environment is disclosed. The invention allows the suspension of jobs in a preempt-able set and the transfer of their respective resources, e.g. either hardware or software resources, to jobs in a preempting set. These activities are performed, all while assuring fairness among jobs scheduled to be executed and optimizing the use of available resources. In a preferred embodiment, the preempt-able and the preempting sets may include jobs characterized by, for example, job priorities, job ownership, or combinations thereof.