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In this paper, we study a joint opportunistic subchannel and power-scheduling problem in relay-based orthogonal frequency-division multiple-access (OFDMA) networks. In most previous works on relay-based networks, immediate relaying at relay stations (RSs) without allowing opportunistic scheduling at RSs was considered. Under this strategy, each RS should transmit the received data from the base station (BS) to the corresponding mobile stations (MSs) immediately within a single time slot, and thus, the effective data rate of the two-hop transmission (BS-RS and RS-MS links) is limited by the achievable data rate of the link with a worse channel state between the two links, resulting in a waste of radio resources. However, if opportunistic scheduling is allowed not only at the BS but at each RS as well, then more efficient radio resource allocation could be possible. Considering time-varying wireless channels, we formulate a stochastic optimization problem that aims at maximizing the average sum rate of the system while satisfying the quality-of-service (QoS) requirement of each MS. By solving the problem, we develop a joint opportunistic subchannel and power-scheduling algorithm for transmission at both the BS and the RSs. Numerical results show that the proposed scheduling algorithm can significantly improve system performance by allowing opportunistic scheduling at both the BS and the RSs.