The kinetics of pulsed cathodoluminescence of Nd3+ ions in single crystals, ceramics, and nanopowders of Nd3+:Y3Al5O12 (Nd3+:YAG) and Nd3+:Y2O3 under excitation by a 2 ns electron beam with average electron energies of 130, 150, and 170 keV was studied. In this case, the luminescence of these substances occurs after the termination of the electron beam. In Nd3+:YAG, there are optical transitions from the 2F25/2 level of the neodymium ion in the ultraviolet and visible regions of the spectrum, as well as from the 4F3/2 level in the near infrared region. In Nd3+:Y2O3, there are not transitions from the 2F25/2 level of the neodymium ion, but infrared luminescence occurs from the 4F5/2 and 4F3/2 levels. The luminescence kinetics is characterized by rise and decay and it is described by the difference of two exponential functions. It is found that the characteristic luminescence decay times are the lifetimes of the 2F25/2, 4F5/2 and 4F3/2 emissive levels, and the rise time is determined by their pumping in recombination and relaxation processes. The rise mechanisms of pulsed cathodoluminescence are substantially different from the mechanisms of "phosphor ignition", which occur during ionization and excitation of the phosphor by an external source.