This paper studies the fairness with which competing flows share the channel in ad hoc networks using collision avoidance protocols. It is shown that the required multi-hop coordination makes the backoff-based distributed fair queueing schemes less effective. Using extensive simulations of two competing flows with different underlying network configurations, it is shown that the commonly used flow contention graph is insufficient to model the contention among nodes and that various degrees of unfairness can take place. The fairness problem is more severe in TCP-based flows due to the required acknowledgment traffic, and TCP throughput is also negatively affected. A measurement-based fair scheme is analyzed in which nodes estimate their fair share of the channel from overheard traffic and adjust their backoff window accordingly (voluntarily); it is shown that such a scheme achieves much better fairness but sacrifices too much throughput. These results indicate that more explicit information exchange among contending nodes is mandatory to solve the fairness problem conclusively while maintaining reasonable throughput.