The mechanism for the formation of the inverse electron distribution function is proposed and real- ized experimentally in a nitrogen plasma of a hollow-cathode glow discharge. It is shown theoretically and experimentally that, for a broad range of the parameters of an N 2 discharge, it is possible to form a significant dip in the profile of the electron distribution function in the energy range e = 2-4 eV and, accordingly, to pro- duce the inverse distribution with df ( e )/ d e > 0. The formation of a dip is associated with both the vibrational excitation of N 2 molecules and the characteristic features of a hollow-cathode glow discharge. In such a dis- charge, the applied voltage drops preferentially across a narrow cathode sheath. In the main discharge region, the electric field E is weak ( E < 0.1 V/cm at a pressure of about p ~ 0.1 torr) and does not heat the discharge plasma. The gas is ionized and the ionization-produced electrons are heated by a beam of fast electrons (with an energy of about 400 eV) emitted from the cathode. A high-energy electron beam plays an important role in the formation of a dip in the profile of the electron distribution function in the energy range in which the cross section for the vibrational excitation of nitrogen molecules is maximum. A plasma with an inverted electron distribution function can be used to create a population inversion in which more impurity molecules and atoms will exist in electronically excited states. © 2001 MAIK "Nauka/Interperiodica".