In this letter, we propose an overlaid hybrid division duplex (HDD) concept for cellular systems which divides a cell into inner and outer regions and utilizes the merits of both time division duplex (TDD) and frequency division duplex (FDD). The proposed system can take advantage of both TDD and FDD without handover between two duplex schemes. Moreover, it is shown that the proposed HDD system outperforms the conventional TDD or FDD system with mobile relay stations when the synchronization issue is considered in orthogonal frequency division multiple access systems. Thus, the proposed overlaid HDD can be considered as a new framework for future cellular systems.