A perturbation theory and numerical solution, based on the unsteady full potential equation, were developed to calculate the unsteady transonic flow field over blunt and pointed bodies of revolution performing harmonic oscillatory motions at zero incidence. Calculations were performed for pulsatile oscillations for a hemisphere-cylinder and pitching oscillations for an ogive-cylinder, an ellipse-cylinder, a hemisphere-cylinder, and a parabolic arc nose. Comparison between theory and experiments was made for the surface pressure distribution at quasi-steady state and for the static and dynamic stability derivatives. (Author).