AbstractThe equation governing the behaviour of two‐dimensional waves in a horizontal stably stratified shearing air current is set up. It is shown that it may be obtained by considering the limit as the number of a set of superposed statically‐neutral layers, each of constant stream velocity, tends to infinity, but that the properties may differ considerably if the number of layers is few.If stable waves occur then at no level do they travel with the same velocity as the air. If unstable waves occur the surfaces containing the wave crests may be so inclined to the vertical as to limit the growth of the waves. Some remarks are made concerning the difficulties of discussion of unstable waves in the general c