Although mesoscale fluctuations of wind and temperature in the free atmosphere have been observed for many years, there is not yet any consensus on the processes that cause them. In this paper it will be shown that the power spectra of mesoscale wind fluctuations from the inertial period (12 to 24 hours in middle to high latitudes) to the buoyancy or Brunt-V¿is¿l¿ period (5 to 10 minutes in the troposphere and lower stratosphere) and in corresponding ranges of horizontal and vertical wavelengths can be described in terms of a universal spectrum of internal gravity or buoyancy waves. This spectrum is a slight modification of the universal spectrum successfully introduced by Garrett and Munk (1972, 1975) to describe the mesoscale (or fine-structure) spectra of parameters in the ocean. (Hereafter papers by Garrett and Munk will be denoted GM).