In this paper, we study an opportunistic power scheduling problem in relay-based OFDMA cellular networks. In most previous works on relay-based cellular networks, scheduling at relay stations (RSs) is not allowed. Hence, each RS should immediately transmit all the received data from the base station (BS) in the first phase in a time-slot to mobile stations (MSs) in the second phase in the same time-slot. In this strategy, the effective data rate of the two-hop transmission (BS-RS and RS-MS) is limited to the rate of the link with worse channel state among two links. Hence, in those systems, even though opportunistic scheduling is allowed in the BS, time-varying channel state of each link cannot be fully exploited, which may result in wastes of radio resources. However, if opportunistic scheduling is allowed not only at the BS but also at each RS, the BS and each RS can fully exploit time-varying channel state of each link, so that more efficient radio resource allocation is possible. We formulate a stochastic optimization problem that aims at maximizing the average sum-rate of relay-based networks where the time-varying wireless channel is modeled as a stochastic process. By solving the problem, we develop an optimal power scheduling algorithm which can be implemented in a distributed manner at the BS and each RS. Simulation results show that by allowing opportunistic scheduling at both the BS and RSs, we can improve system performance more significantly.