Considerable attention has recently been paid to the study of so-called “secondary” acoustic-gravity waves (AGWs) that arise as a result of instability and nonlinear interactions of “primary” wave modes propagating from atmospheric sources, among themselves, and with the mean flow. In this paper, for the first time, the horizontal spatial spectra of primary and secondary AGWs are separated at fixed altitude levels in the middle and upper atmosphere at different time moments, which are simulated using a three-dimensional nonlinear high-resolution model AtmoSym. It is shown that in a short time after switching on the plane wave source at the lower boundary of the model, the spectrum consists of a peak corresponding to primary AGW and quasi-white noise generated by random atmospheric disturbances and the numerical model. Later, secondary peaks appear in the spectra at horizontal wave numbers, which are multiples of the wave numbers of primary AGW. The proposed separation of the spectra of primary and secondary AGWs makes it possible to estimate the relative contribution of secondary AGW at different altitudes, at different times, and with different stability of background temperature and wind profiles in the atmosphere.