Abstract: We study three-body systems composed of D(*), B(*), and (B) over bar(*) in order to look for possible bound states or resonances. In order to solve the three-body problem, we use the fixed center approach for the Faddeev equations considering that the B*(B) over bar*(B (B) over bar) are clusterized systems, generated dynamically, which interact with a third particle D((D) over bar) whose mass is much smaller than the two-body bound states forming the cluster. In the DB*(B) over bar*, D*B*(B) over bar*, DB (B) over bar, and D*B (B) over bar systems with I = 1/2, we found clear bound state peaks with binding energies typically a few tens MeV and more uncertain broad resonant states about ten MeV above the threshold with widths of a few tens MeV.