The first and second-order Raman spectra were measured for single-wall carbon nanotubes (SWNTs). Eighteen first-order Raman spectral lines and seven second-order Raman spectral lines were observed. Spectral lines predicted by theory were almost fully detected. Positions of the spectral lines observed are well coincident with theoretical values. The number of Raman active phonon modes and the second-order Raman spectral lines for high-purity SWNTs observed is the biggest up to date.