The laminar-boundary-layer flow about a cone at large angles of attack to a supersonic stream has been analyzed in the plane of symmetry. At the bottom of the cone, velocity profiles were obtained showing the expected tendency of the boundary layer to become thinner on the under side of the cone as the angle of attack is increased. At the top of the cone, the analysis failed to yield unique solutions, except for small angles of attack. Beyond a certain critical angle of attack, boundary-layer flow does not exist in the plane of symmetry, thus indicating separation.