Subchannel allocation schemes for OFDMA (orthogonal frequency division multiple access) systems with adaptive transmission are investigated. The analysis involves two scenarios: single-hop transmission and dual-hop relaying transmission. The overall objective is to utilize minimum system resource (in terms of subchannel) while satisfying scheduled users' data rate requirements under a certain error rate performance restriction. The ordered subchannel selection with adaptive modulation scheme is applied to both cases. In single-hop case, a low-complexity greedy subchannel allocation algorithm with two options is proposed, depending on whether a common modulation mode is applied on all selected subchannels or not. The resulting two options are termed as GS-FA (greedy selection with full adaptivity) and GS-LA (greedy selection with limited adaptivity), respectively. In dual-hop relaying case, two relaying schemes are considered: Amplified-and-Forward (AF) and Decode-and-Forward (DF). Based on this, four different combinations of relaying schemes and ordered subchannel selection with adaptive modulation scheme are investigated: DF with full adaptivity (DF-FA), AF with full adaptivity (AF-FA), AF with limited adaptivity (AF-LA), and AF with limited adaptivity and subchannel mapping (AF-LA with SCM). For both single-hop and dual-hop relaying case, performances of different proposed schemes are evaluated through mathematical analysis and compared with selected numerical results.