The last decade has seen significant advances in the technological sophistication of wireless networks. The most widely used method for data transmission in such networks is known as orthogonal frequency-division multiplexing (OFDMA), which owes its popularity, among other thing, to its use in the LTE mobile standard. In cases in which direct transmission between a source and destination is impossible, so-called relay stations are used. Networks employing relay stations are referred to as relay networks. The thesis begins with a short introduction to OFDMA and relay networks. Using the so-called amplify-and-forward method in OFDMA relay networks, pro- blems of subcarrier and power allocation, as well as fairness, arise. The thesis considers a system with a single source, relay and destination station serving multiple users. The algorithm presented in the thesis uses subcarrier grouping into chunks, which is made possible by the high correlation of contiguous subcarriers, and offers a significant speed-up of the algorithm and a reduction in signalling overhead. Subcarrier matching on the relay is accomplished on a chunk basis. The allocation of chunks to users is also calculated, as is the power allocation on the relay, with the goal of achieving fairness and maximizing the data rate. The single-subcarrier approach is used as a benchmark and it is shown that the proposed algorithm achieves very good results even with a relatively large chunk size.