This paper describes new algorithms, not previously available, for predicting atmospheric absorption of sound at high altitudes. A basis for estimating atmospheric absorption up to 160 km is described. The estimated values at altitudes above 90 km must be considered as only approximate due to uncertainties about the composition of the atmosphere above 90 km and simplifying assumptions. At high altitudes, classical and rotational relaxation absorption are dominant, as opposed to absorption by molecular vibrational relaxation that is the principle atmospheric absorption loss mechanism for primary sonic booms propagating downward from a cruising supersonic aircraft. Classical and rotational relaxation absorption varies inversely with atmospheric pressure, thus increasing in magnitude at high altitudes as atmospheric pressure falls. However, classical and rotational losses also relax at the high values of frequency/pressure reached at high altitudes and thus, for audio and infrasonic frequencies, begin to decrease at altitudes in the range of 80–160 km. This paper includes: (1) modifications to the existing algorithms in the ISO/ANSI standards for atmospheric absorption at high altitudes, and (2) algorithms for definition of mean atmospheric conditions, including humidity content at high altitude conditions. Also included are suitable values for the temperature-dependent physical parameters of the atmosphere, viscosity, and the specific heat ratio, involved in defining atmospheric absorption at temperatures found at high altitudes. It has been found that carbon dioxide plays a major role in the relaxation of O2 and N2 at high altitudes due to the absence of H2O. Molecular relaxation by CO2, not covered by the current ANSI or ISO standards, is the dominant source of molecular relaxation absorption at altitudes above 60 km at frequencies of 1 Hz and above 10 km at a frequency of 10 kHz. However, at such high altitudes, classical plus rotational losses dominate reaching maximum values at 80–160 km, depending on frequency. In this regime, vibrational relaxation is less important. More accurate predictions of absorption at altitudes above 90 km would require more sophisticated models for the variation in atmospheric viscosity and specific heat ratio above such altitudes. © 2004 Acoustical Society of America.