The spectra of C60 and C70 thin films over a wide energy range (0.6 to 6.5eV) are measured by transmission spectroscopy and photothermal deflection spectroscopy (PDS), and the optical absorption coefficients are obtained. The optical transitions for the C60 and C70 thin films are analyzed according to the molecular orbital model. The weak absorption spectra of the fullerenes are similar to that of amorphous silicon. The optical energy gaps are given by Tauc's plots as 1.75 and 1.65eV for C60 and C70 thin films, respectively. The disorders in the fullerene films, which resulted in band-tail state or defect state, are indicated by Urbach edge and sub-gap absorption. It is the disorder that brought the difficulty in determination of the energy gap for fullerenes. The effects of the deflection medium and substrate on the weak absorption spectra of fullerene films are also discussed.