The fundamental difference is that wireless networks are of a broadcast nature. There is no strict notion of a ‘link’, since transmissions from nearby nodes interfere with each other. We consider a fairly general model of interference in wireless networks, and present a counterexample of a wireless network in which the congestion control mechanism has an unstable equilibrium point at the desired fair solution. ns-2 simulations of this counterexample manifest an oscillatory throughput behaviour that is orders of magnitude worse than the corresponding wired networks. Surprisingly, this oscillatory throughput behaviour appears to be fairly typical of simulations in wireless networks, with almost all randomly chosen network simulation examples manifesting it. This loss of stability leads us to suggest that perhaps TCP should be modified for use in wireless networks, and that a cross-layer redesign of wireless TCP and MAC is needed to explicitly account for the effects of the wireless nature of interference.