Formal specification of multi-threaded programs is notoriously hard, because thread execution may be preempted at any point. In contrast, abstract concurrency models such as actors seriously restrict concurrency to obtain race-free programs. Languages with cooperative scheduling occupy a middle ground between these extremes by explicit scheduling points. They have been used to model complex, industrial concurrent systems. This paper introduces cooperative contracts, a contract-based specification approach for asynchronous method calls in presence of cooperative scheduling. It permits to specify complex concurrent behavior succinctly and intuitively. We design a compositional program logic to verify cooperative contracts and discuss how global analyses can be soundly integrated into the program logic.