Coupling internal inverse and forward models gives rise to on-line simulation processes that may be used as a common computational substrate for action execution, planning, recognition, imitation and learning. In this paper, multiple coupled internal inverse and forward models are arranged in a hierarchical fashion, with each level of the hierarchy interacting with other levels through top-down and bottom-up processes. Through experiments involving imitation of a human demonstrator performing object manipulation tasks, this architecture is shown to equip a robot with a multi-level motor abstraction capability. This is then used to solve the correspondence problem in action recognition. The architecture is inspired by biological evidence.