A method of determining the surface flow velocities for arbitrary pointed bodies of revolution in complex supersonic flow, j.e., flow due te constant incidence, constant pitching velocity and constant lateral acceleration, has been derived and a corresponding numerical procedure developed . The method is based on a solution suggested by M. J. Lighthill for the symmetrical flow case. Good correspondence between results of the present methad with available " exact", and exact linear results for cones has been found for the range 0 to 1 of the similarity parameter ßτ. Using the exact isentropic pressure - velocity relation, expressions for the limiting value of the pressure coefficient derivatives as the independent