In the paper, we show that the spectrum of acoustic-gravity waves in an isothermal atmosphere includes four specific evanescent modes. These modes are the solutions of the system of hydrodynamic equations for small atmospheric disturbances under the assumption that one of the quantities (horizontal or vertical components of particle velocity, density fluctuations, or temperature) is equal to zero. Three of the four specific modes (the Lamb wave, the Brunt-Väisälä oscillation, and the f-mode) are well known, but they were previously obtained as independent solutions.

         The recent discovery by the authors of the evanescent γ-mode made it possible to show that all four specified modes form a certain family of special modes of the isothermal atmosphere. On the spectral diagram of the frequency and the wave vector, there are four dispersion curves of these special modes in which one of the perturbed quantities is equal to zero. These curves belong to the evanescent region of the acoustic-gravity wave spectrum. They intersect each other at five points. It is shown that the specific modes cannot interact at the intersection points. The polarization ratios between two perturbed quantities have a different sign on either side of a particular curve if one of the quantities on this curve is zero. These properties can be used as indicators of the specific modes in experimental studies of the evanescent spectrum of AGWs. By using polarization relations, the possibility of observing these modes in the Earth’s atmosphere and on the Sun is also analyzed.