In monatomic plasmas excited by high‐intensity relativistic electron beams, the electron secondary distribution function is dominated by elastic electron‐electron collisions at low electron energies and by inelastic electron‐atom collisions at high electron energies (above the excitation threshold). Under these conditions, the total rate of excitation by inelastic collisions is limited by the rate at which electron‐electron collisions relax the distribution function in the neighborhood of the excitation threshold. To describe this effect quantitatively, an approximate analytic solution of the electron Boltzmann equation is obtained, including both electron‐electron and inelastic collisions. The result provides a simple formula for the total rate of excitation.