Methods have been developed to solve the problem of laminar boundary layers on sharp and spherically blunt cones at angle of attack to nonuniform supersonic free streams. A three-dimensional boundary-layer solution is used to solve sharp cone problems and the afterbody of blunt cone problems. An axisymmetric boundary layer solution is used to solve the axisymmetric region of blunt cones. An interpolation method has been developed enabling the use of axisymmetric solution data as starting data for the three dimensional boundary layer solution on a blunt cone. An existing implicit finite-difference numerical scheme was used to solve both the axisymmetric and three-dimensional boundary-layer equations. Edge properties for a sharp cone and for the afterbody of a blunt cone come from method of characteristics solutions of the inviscid flow field. A modified inverse method for solving the inviscid flow field is used to provide edge properties for the axisymmetric region of blunt cones. Results obtained for blunt cones in uniform flow are compared to experimental data with. good agreement. Uniform flow results for sharp cones are compared to experimental data and to existing numerical data. Skin friction and heat transfer data obtained for sharp and blunt cones in nonuniform flow fields show a departure from the uniform flow values. Normalized skin friction and heat transfer coefficients for a sharp cone in two dimensional shear flow increase downstream relative to conical flow values. The effect of wake flow on a blunt cone is to increase the heat transfer considerably, relative to uniform flow values. Downstream values of skin friction are shown to fall below uniform flow values. Decreasing the width of the wake causes more severe departure from uniform flow values, for both skin friction and heat transfer on blunt cones. The presence of free-stream nonuniformities hastened the onset of separation particularly in the blunt cone cases. The beginning of separation occurred sooner in both the longitudinal and transverse planes. Smaller width wakes and higher angles of attack caused earlier onset of separation. / Master of Science