Processes that compete for the use of scarce resources may maneuver themselves into a deadlock situation. The paper establishes two necessary and sufficient conditions that guarantee the absence of deadlock under the expedient allocation policy. Their equivalence is proved. It is shown that the condition for deadlock-freedom is just another form of the well- known condition for the existence of systems of distinct representatives as expressed in the König-Hall theorem. For binary resources deadlock- freedom turns out to be equivalent to the absence of cycles in hypergraphs. It is furthermore interesting that, in contrast to earlier work, the condition for deadlock-freedom is proved without using König- Hall or equivalent theorems.