Abstract. Spin glasses are highly disordered systems and their out-of-equilibrium dynamics have age dependent decorrelation properties, a phenomena known as {\it aging}. Physicists predict that for a large class of models the energy landscape has a hierarchical structure in the limit. As a first attempt to understand this hierarchical structure on the dynamics we introduce the so-called GREM-like trap models. We prove the existence of various time scales where the system ages with different aging functions. (Joint work with V. Gayrard.)