Auxin underlies many processes in plant development and physiology, and this makes it of prime importance to understand its movements through plant tissues. In stems and coleoptiles, classic experiments showed that the peak region of a pulse of radio-labelled auxin moves at a roughly constant velocity down a stem or coleoptile segment. As the pulse moves it becomes broader, at a roughly constant rate. It is shown here that this spreading rate is larger than can be accounted for by a single channel model, but can be explained by coupling of channels with differing polar transport rates. An extreme case is where strongly polar channels are coupled to completely apolar channels, in which case auxin in the apolar part is dragged along by the polar part in a somewhat diffuse distribution. The behaviour of this model is explored, together with others that can account for the experimentally observed spreading rates. It is also shown that saturation of carriers involved in lateral transport can explain the characteristic shape of pulses that result from uptake of large amounts of auxin. 