a b s t r a c tExascale computing is fast becoming a mainstream research area. In order to realize exascale performance, it is necessary to have efficient scheduling of large parallel computations with scalable performance on a large number of cores/processors. The scheduler needs to execute in a pure distributed and online fashion, should follow affinity inherent in the computation and must have low time and message complexity. Further, it should also avoid physical deadlocks due to bounded resources including space/memory per core. Simultaneous consideration of these factors makes affinity driven distributed scheduling particularly challenging. We attempt to address this challenge for hybrid parallel computations which contain tasks that have pre-specified affinity to a place and also tasks that can be mapped to any place in the system. Specifically, we address two scheduling problems of the type P m |M j , prec|C max . This paper presents online distributed scheduling algorithms for hybrid parallel computations assuming both unconstrained and bounded space per place. We also present the time and message complexity for distributed scheduling of hybrid computations. To the best of our knowledge, this is the first time that distributed scheduling algorithms for hybrid parallel computations have been presented and analyzed for time and message bounds under both unconstrained space and bounded space.