We address the problem of radio resource allocation in the Downlink (DL) of a cellular system with Relay Stations (RS), based on Orthogonal Frequency Division Multiple Access (OFDMA) transmission technology. There is a need for the design of resource allocation algorithms for this type of system, where practical yet efficient algorithms are required to exploit the potential capacity and coverage increase offered by the relays. We propose several resource allocation algorithms with different options such as time or frequency division. The evaluations give some directions about the suitable allocation schemes. One algorithm offers an overall improvement of throughput and coverage, compared to a system without relays. At the same time, the advantage of our algorithms is that their complexity and amount of information overhead are much reduced compared to an optimal algorithm.