This paper aims at broadening the scope of hierarchical ATPG to the behavioral-level The main problem of using behavioral information for ATPG is the mismatch of timing models between the behavioral- and gate-levels. Theoretical analysis shows that the definition of the concept of dominated sequences captures the needed link between the levels. To validate the concept correctness, and to show how it can be profitably exploited, a prototypical hierarchical ATPG is presented, and experimental results show that the performance of a simple ATPG algorithm that is able to exploit behavioral information is much higher than a much more sophisticated gate-level tool.