The manner in which fluid driven through a channel of width a responds in anticipation of a severe asymmetric distortion (e.g. to the wall or interior conditions downstream) is discussed when the oncoming flow is fully developed, the characteristic Reynolds number K is large and the whole motion remains laminar. Far ahead of the disturbance, at distances $O(aK^{\frac{1}{7}})$, there occurs a free interaction which triggers a small displacement in the core, generating viscous layers near both walls; the relatively large induced pressure gradient acting across the channel is then found to sustain the growth of this displacement. Numerical solutions of the fundamental nonlinear problem show that one layer separates in a regular fashion, but that beyond separation the other layer, under compression, produces a singularity in the interaction. Analysis of the singularity based on a self-similar structure in the partly reversed flow then leads to a description of the nonlinear flow features nearer the distortion which seems to have strong physical significance. The major implication is that the flow will have already separated at one wall, and developed a definite nonlinear character quite distinct from that of the original Poiseuille flow, long before it reaches finite distances from the distortion. The separation point is predicted to be a distance $0.49 aK^{\frac{1}{7}} (+ O(a))$ ahead of the particular finite distortion. Comparisons of this and other predictions with computed solutions of the full Navier–Stokes equations show reasonable agreement.