Abstract The problem of stability of laminar flow in two dimensions is reducible, as is well known, to the integration of a fourth-order differential equation containing a large parameter. The equation has two slowly varying and two rapidly varying integrals; and because of the presence of a large parameter it is necessary to find the asymptotic expansions of these integrals. The main difficulty of the problem consists in finding the transformations of these integrals through the critical points, particularly of the slowly varying integrals. This problem was first attacked by Heisenberg (1924), and the solution improved by Tollmien (1929); their result was tested numerically by Schlichting (1935, p. 59), and the question was recently reconsidered by Lin (1945,1946) and Tollmien (1947). The application of Tollmien’s theory to the problem of stability of the laminar boundary layer on a plane, worked out in great detail by Schlichting (1933, 1935), was recently tested experimentally by Schubauer & Skramstad (1947), and a good agreement was obtained.