It is pointed out that there are two separate mechanisms for upstream influence through the boundary layer in supersonic flow, and that one of these (that involving separation) operates also in subsonic flow. A quantitative theory of subsonic flow up a step is given to illustrate this. The main differences between the subsonic and supersonic flows are as follows: (i) The boundaries of dead-air regions are nearly straight in supersonic flow but are usually highly curved in subsonic flow. (ii) Separation (whether of the laminar or turbulent layer) occurs at a much lower pressure coefficient in supersonic flow; this is only slightly due to the fact that the fluid nearest the wall is then lighter and so more easily brought to rest; it is due much more to the relative suddenness of the pressure rise ahead of the dead-air region. (iii) However, for a given pressure coefficient in the dead-air region, the distance of upstream influence is somewhat greater in the subsonic flow, except at the highest pressures. A qualitative discussion of the second mechanism of upstream influence, in supersonic flow, is given; for a quantitative theory of this see part II (Lighthill 1953).