The focus of this talk is to present and discuss scheduling strategies in the context of hybrid parallel multi-core platforms composed of multicores with accelerators (GPUs). We put emphasis on general purpose policies developed at the middleware level (by opposition to codes tuned by the expert users for specific applications). We survey several recent results in various situations (off-line/on-line scheduling, for both independent tasks and precedence relations). These results are illustrated by actual experiments on the comparison of biological sequences in large databases.