Title: Static and Dynamic Execute After relationships as a replacement of dependence-based program slices Abstract: We present our recent research on the so-called Execute After dependencies, which are - in essence - control flow-based dependencies that do not take into account data-flow information. These dependencies can be used to compute "conservative program slices" which approximate slices computed by System Dependence Graph-based algorithms. Due to this simplification the approach is really scalable compared to the SDG-based slicers. At the same time, the precision declines only very slightly, by some 4% on average, while much larger difference would be expected. We experimented with dependencies on different levels from statement, through procedure to class level, and with static and dynamic variants as well. Some extensions to specific architectures, like database systems and applications in impact analysis and testing are sketched as well.