Multiwall carbon nanotubes are produced by decomposition of acetylene at 600 degreesC on metal catalysts supported on NaY zeolite. The support and the metal are eliminated by dissolving them in aqueous hydrofluoric acid (HF). Two methods were used to eliminate the pyrolitic carbon: oxidation in air at 500 degreesC and oxidation by potassium permanganate in acidic solution at 70 degreesC. The progress and efficacy of the purification methods are verified by TEM. The properties of the purified multiwalled carbon nanotubes are probed using C-13 and Xe-129 NMR spectroscopy under continuous-flow optical-pumping conditions. Xenon is shown to penetrate the interior of the nanotubes. A distribution of inner tube diameters gives rise to chemical shift dispersion. When the temperature is lowered, an increasing fraction of xenon resides inside the nanotubes and is not capable of exchanging with xenon in the interparticle space. In the case of the permanganate-oxidized sample, rapid xenon relaxation is attributed to interaction with residual MnO2 nanoparticles in the interior of the tubes.