We investigate the orbital dynamics of small dust particles generated via the continuous micrometeoroid bombardment of the Martian moons. In addition to Mars's oblateness, we also consider the radiation pressure perturbation that is complicated by the planet's eccentric orbit and tilted rotational axis. Considering the production rates and the lifetimes of dust grains, we show that particles from Deimos with radii of about 15 μm are expected to dominate the population of a permanently present and tilted dust torus. This torus has an estimated peak number density of ≂5¿10-12 cm-3 and an optical depth of ≂4¿10-8.