The IEEE802.16j standard uses non-transparent relay stations to extend coverage. There are two types of non-transparent relay modes, that is, the time-division transmit and receive (TTR) relay mode which can operate with one of two types of frame structures, a single-frame and multiframe structure, and the simultaneous transmit and receive (STR) relay mode. In this paper, we analyze the relay performance of TTR and STR relay modes in IEEE 802.16j MMR system. We also propose a fair resource allocation scheme for the downlink relay frame. Numerical results show that relay performance of the TTR with a single-frame or a multiframe structure and that of the STR relay modes are almost the same in a two-hop system. However, in a three-hop system, the TTR mode with a single-frame structure outperforms other relay modes.