IR and Raman spectra of two fluorofullerenes, C60F48 and C60F36, are thoroughly studied. Assignment of the experimental spectra is provided on the basis of density functional theory (DFT) computations. Perfect correspondence between experimental and computed spectra enabled us to confirm that the major isomer of C60F48 has D3 symmetry. It was found that as-synthesized samples of C60F36 consist mainly of C3 and C1 isomers in ca. 2:1 ratio and 2-3% of T-symmetric structures. Extensive AM1 and DFT computations have shown that all three structures are the most stable isomers of C60F36. Previous structural assignment of the C3 isomer (Gakh, A. A.; Tuinman, A. A. Tetrahedron Lett. 2001, 42, 7137-7139) was confirmed by the vibrational data.