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Our earlier work (Weber et. al., Trans. Info. Theory, Dec, 2005) introduced transmission capacity as the maximum spatial density of concurrent transmissions in an ad hoc network subject to a QoS constraint on the outage probability. That work computed the transmission capacity under a simple path loss channel model. Recent work (Weber et. al., submitted to the 2006 SPASWIN workshop) has studied lower and upper bounds on the outage probability for a fairly general class of channel models, including path loss, shadowing, and fast fading effects. In this work we derive expressions for the the transmission capacity under this same general class of channel models. It is shown that random channel effects tend to degrade the transmission capacity, and that the limiting factor in the transmission capacity is the presence of interfering nodes in close proximity to receivers (the near far problem).