<p>We study various wave oscillations that can occur in plasma–dust systems of meteoroid tails. In particular, taking into account the inhomogeneity of the plasma density of meteoroid tails and the presence of the Earth’s magnetic field, the excitation of lower-hybrid drift waves, as well as the development of modulation instability of these oscillations, are possible. The appearance of electrophonic sounds simultaneously with the passage of meteoroids can be caused by the development of lower-hybrid drift turbulence in meteoroid tails. Conditions under which lower-hybrid drift waves can propagate in the plasma of meteorid tails as meteorids pass in the Earth’s ionosphere, as well as the development of the modulation instability of these waves in various frequency ranges, are considered. The corresponding growth rates of the modulation instability of a monochromatic pump wave are derived. The values of the growth rates of this instability for typical parameters of the plasma of meteoroid tails are calculated. It is shown that in the considered system of meteoroid tails in the Earth’s atmosphere the development of the Drummond–Rosenbluth instability and the occurrence of anomalous resistance are possible under certain configurations of the Earth’s magnetic field relative to the plasma of meteorid tails. It is shown that the considered processes have time to develop over typical lifetimes of meteoroid tails.</p>