A novel method for the purification of single-walled and multiwalled carbon nanotubes is described. The method involves acid washing followed by hydrogen treatment in the 700-1000degreesC range. While acid washing dissolves the metal particles, the hydrogen treatment removes amorphous carbon as well as the carbon coating on the metal nanoparticles. The high quality of the nanotubes obtained after purification has been checked by electron microscopy, X-ray diffraction, and spectroscopic methods.