Lasing on a self-terminating transition 2(1)P(1)degrees-2(1)S(0) (lambda = 2.058 mu m) in helium atom is studied for a single-and double-pulse operation regimes under electron beam pumping in pure helium and its mixtures with H-2, N-2, O-2, CO2, H2O, NH3, and N2O. In pure helium, the maximal pulse duration is similar to 50 ns, which agrees with the calculated value. Recovery of lasing in the second pulse is observed at a time delay between the pulses of longer than 1.25 mu s. In adding CO2, N2O, NH3, and H2O, the relaxation rate for population of the metastable state He(2 S-1(0)) increases, which makes the delay, needed for recovering lasing, shorter up to pulse merging in the case of H2O. At the exciting pulse base-level duration of 1.2 ms, in mixtures of helium with NH3 and H2O, laser pulses with a duration of similar to 0.8 mu s are observed, which testifies that collisional quasi-cw lasing occurs. Mechanisms of collisional lasing are discussed.