We calculate low-frequency gyrotropic excitation modes of the skyrmion state thin 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. We consider Bloch and Neel-type magnetic skyrmions and assume that the dot magnetization does not depend on the thickness coordinate. The skyrmion gyrotropic frequencies are calculated in GHz range as a function of the skyrmion equilibrium radius, dot radius and the dot magnetic parameters. The magnetostatic interaction is explicitly accounted via appropriate ansatz of the skyrmion magnetization. Recent experiments and calculations of magnetic skyrmion dynamics in infinite thin films and nanodots are discussed.