Summary: Investigations of wave and vibration properties of single- or multi-walled carbon nanotubes based on nonlocal beam models have been reported recently [see e.g. Y. Q. Zhang et al., Phys. Rev. B 71, 195404 (2005)]. However, there are numerous inconsistencies in handling of governing equations, applied forces and boundary conditions based on some of the reported nonlocal beam models. In this paper, the consistent equations of motion for nonlocal Euler and Timoshenko beam models are provided, and some issues on nonlocal beam theories are discussed. The models are then applied to the studies of wave properties of single- and double-walled nanotubes, including scale effects.