Raman spectra of the fullerenes C60 and C70 have been measured for photon energies from 2.1 to 3.6 eV. Resonant enhancement of the Raman cross section versus wavelength has been measured for the 270, 497, 1424, 1469, and 1568 cm-1 lines, with the diamond 1332 cm-1 line as a reference. A prominent enhancement occurs near 2.4 and 2.5 eV for the C60 497 cm-1 and 1469 cm-1 lines, respectively. The C70 1424 cm-1 and 1568 cm-1 lines increase monotonically in intensity between 2.3 and 2.7 eV. The 270 cm-1 line, which has contributions from both C60 and C70, exhibits resonance enhancement which is qualitatively similar to that of the C70 lines. All of the lines show resonance enhancement at 3.4 and 3.5 eV.