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Existing medium access control (MAC) schemes for wireless local area networks (WLAN) have been shown to lack scalability in crowded networks, and efficiency in supporting heterogeneous traffic types. These issues are mostly due to the use of random multiple access techniques in the MAC layer. The design of these techniques is highly linked to the choice of the underlying physical (PHY) layer technology. The advent of new PHY schemes that are based on orthogonal frequency division multiple access (OFDMA) provides new opportunities for devising more efficient MAC protocols. We propose a new adaptive MAC design based on OFDMA technology. The design uses OFDMA to reduce collision during transmission request phases, and makes channel access more predictable. To improve efficiency, we combine the OFDMA access with a carrier sense multiple access (CSMA) scheme. Data transmission opportunities are assigned through an access point that can schedule traffic streams in both time and frequency (subchannels) domains. We demonstrate the effectiveness of the proposed MAC and compare it to existing mechanisms through simulation experiments and by deriving an analytical model for the operation of the MAC in saturation mode.