The results of studying the dynamics of molecules of solutions of fullerene C60 in benzene and toluene are presented. The studies were carried out by the method of quasi-elastic scattering of slow neutrons. The following were determined: the total self-diffusion coefficient D, its collective Dcoll and single-particle Ds-p contributions, and molecule relaxation time τ0 before and after the dissolution of fullerene. It is necessary to pay attention to the fact that in our case a kind of neutron contrast experiment takes place. The significant difference (more than ten times) in the cross-sections for an incoherent scattering of neutrons by hydrogen and carbon nuclei made it possible to obtain diffusion parameters that characterize the dynamics of solvent molecules exclusively. It turned out that the intensity of diffusion movements of solvent molecules is almost ten times higher than the mobility of fullerene molecules.