We calculate gyrotropic excitation modes of the skyrmion ground state in ultrathin cylindrical magnetic dots. The skyrmion is assumed to be stabilized at room temperature and zero external magnetic field due to an interplay of the isotropic and Dzyaloshinskii-Moriya exchange interactions, perpendicular magnetic anisotropy, and magnetostatic interaction. The gyrotropic frequencies of the Bloch- and Néel-type magnetic skyrmions are calculated in the gigahertz range as a function of the skyrmion equilibrium radius, dot radius, and the dot magnetic parameters. Recent experiments and simulations of magnetic skyrmion gyrotropic dynamics in nanodots are discussed.