We study three-body systems composed of D ðÃÞ , B ðÃÞ , andB ðÃÞ 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 ÃBà ðBBÞ are clusterized systems, generated dynamically, which interact with a third particle DðD Ã Þ whose mass is much smaller than the two-body bound states forming the cluster. In the DB ÃBà , D à B ÃBà , DBB, and D à BB systems with I ¼ 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.