The boundary-layer equations in a Crocco variables form have been numerically solved for flow over spinning sharp and blunt cones at zero incidence to supersonic and hypersonic streams. Both laminar and turbulent flows have been treated, and for the blunt cases swallowing of the inviscid entropy layer by the boundary layer has been considered. The item of primary interest is roll damping, and results of a parametric study involving Mach number, Reynolds number, cone angle, and bluntness ratio are presented. Limited comparisons with experimental data and another method of computation are also presented. (Author).