A nonlinear theory for the long-range propagation of sonic booms through the thermosphere has been developed. Arealistic atmosphere is employed, and consideration is given to such factors as nonlinear stretching and decay of the wave, the effects of the caustic, the linear acoustic attenuation, and the increase in Mach number due to the decreasing density at high altitudes, detailed results are presented for the case of the Concorde SST in straight, level and steady flight at 17.5 km and a velocity of Mach 2. We predict maximum ground level pressures of 0.3 Pa with an N-wave period of about 10 seconds. The sound level is a minimum along the flight track with the maximum signal strength occurring about 300 km off the flight track. The strongest received signal travels Initially downward and reflects off the surface of the ocean to thermosphere. The wave turns around at an altitude of 160 km and is returned back to the ground at a horizontal distance of 320 km from the launch point. The acoustic Mach number of the wave never exceeds 0.2. Ninety percent of the wave's energy is attenuated below 100 km with 99% attenuated by the time the wave reaches the turning the turning point. (Author).