The laminar boundary-layer flow about a circular cone at large angles of attack to a supersonic stream has been analyzed in the plane of symmetry by a method applicable in general to the flow about conical bodies. 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. This critical angle is presented as a function of Mach number and cone vertex angle.