Propagation of electromagnetic waves in a random distribution of C60 molecules are investigated, within the framework of the classical electrodynamics. Electronic excitations over the each C60 molecule surface are modeled by a spherical layer of electron gas represented by two interacting fluids, which takes into account the different nature of the π and σ electrons. It is found that the present medium supports four modes of electromagnetic waves, where they can be divided into two groups: one group with shorter wavelength than the light waves of the same frequency and the other with longer wavelength than the free-space radiation.