In the present study, the laser absorption method was used to measure the rates of quenching of the metastable state He(2(1)S(0)), the lower laser level in the self-terminating helium laser, with H2O, NH3, N2O, and CO2 molecules. For the above molecules, the quenching rate constants were found to equal (1.2 +/- 0.3)10(-9), (0.8 +/- 0.2)10(-9), (1.9 +/- 0.2)10(-9) and (2.2 +/- 0.4)10(-9) cm(3) s(-1). Under excitation with long (up to 750 ns) open discharge generated electron beam pulses, lasing on the transition He (2(1)P(1)(0)-2(1)S(0)) was examined. In the mixtures He-H2O and He-NH3, lasing durations almost equal to the pump-pulse duration were obtained. In the mixtures of He with CO2 and N2O, no lasing prolonged in comparison with pure helium was found. The data obtained were explained considering two quenching mechanisms for the state He(2(1)S(0)): in collisions with molecules and in collisions with plasma electrons having low energies due to fast relaxation of the vibrational states of H2O and NH3 molecules. (C) 2011 Elsevier By. All rights reserved.