Using reflection high-energy electron diffraction, we have observed diffraction patterns from both vertically aligned and randomly oriented multiwalled carbon nanotube samples. The patterns, for both samples, consist of rings and are similar to the patterns observed in x-ray diffraction from multiwalled carbon nanotubes. The ring radii are roughly consistent with powder diffraction from graphite. However, the ratio of the interlayer spacing to the in-plane nearest-neighbor distance is, for both samples, higher than the ordered graphite value of 2.36. Also, reflection electron energy-loss spectra were taken for both samples. For the vertically aligned sample, the center-to-center spacing of the nanotubes was determined, from the energy-loss spectrum, to be $52\ifmmode\pm\else\textpm\fi{}12\mathrm{nm}.$