We propose a novel execution model for the implicitly parallel execution of data parallel programs in the presence of general I/O operations. This model is called hybrid because it combines the advantages of the standard execution models fork/join and SPMD. Based on program analysis the hybrid model adapts itself to one or the other on the granularity of individual instructions. We outline compilation techniques that systematically derive the organization of parallel code from data flow characteristics aiming at the reduction of execution mode switches in general and synchronization/communication requirements in particular. Experiments based on a prototype implementation show the effectiveness of the hybrid execution model for reducing parallel overhead.