Abstract <p>Phobos and Deimos are atmosphereless celestial bodies with a weak gravity. Their surfaces consist of small regolith grains that are not connected to one another and have appeared due to bombardment with micrometeorites. Their weak gravity makes these bodies interesting for piloted flights and increases the role of dust, since even a small perturbation leads to the creation of massive dust clouds above their surfaces. The surfaces of these satellites of Mars are charged by the electromagnetic radiation from the Sun and the plasma of the solar wind. The dust grains located at the surface and in the near-surface layer absorb the photons, photoelectrons, electrons, and ions of the solar wind, and, as a result, they obtain electric charge. The action of the electrostatic force under the weak gravity conditions leads to the detachment of dust grains from the surface and the creation of a dusty plasma system together with the electrons and ions. In the dusty plasma system above the surfaces of Mars’s satellites, dust acoustic waves can propagate. In this work, we consider nonlinear periodic and solitary dust acoustic waves with an arbitrary amplitude, which can propagate near the surface of Phobos and Deimos, and discuss the possibility of observing these structures.</p>