An asymptotic description is obtained for the acceleration of a laminar, hypersonic boundary layer approaching a sharp corner, assuming small interaction with the outer inviscid flow. Viscous forces are neglected except in a thin sublayer. The initial part of the expansion takes place over a distance O(Mj), where Me is the external Mach number and d is the boundarylayer thickness. Here the transverse pressure gradient is small and a solution can be obtained analytically. Within a distance O(S) from the corner, the effect of streamline curvature is essential, and a numerical solution is obtained by the method of integral relations for a single strip. The solution for surface pressure is compared with experimental results and with a similar theory for a laminar, supersonic boundary layer approaching a corner, and an approximate velocity profile at the corner is calculated.