Single-walled carbon nanotubes were studied by C-13 nuclear magnetic resonance (NMR). Two types of C-13 nuclear spins were identified with different spin-lattice relaxation rates. The fast-relaxing component, assigned to metallic tubes, followed the relaxation behavior expected in metals, and the density-of-states at the Fermi level increased with decreasing tube diameter. The slow-relaxing component has a significantly lower density-of-states at the Fermi level Exposure to oxygen has a substantial effect on relaxation rates of both components.