Stimulated emission occurs when (ortho- and para-) H2, HD, D2, CO, Ne, and N2 are excited by a 4-GW electron beam. The beam is generated by a Febetron, model 706, and propagates 2.3 m through the gases at 8–100-Torr pressures. Propagation is aided by an externally applied ∼ 10 kG magnetic field. Collisions involving primary, secondary, and cascade electrons transfer ≤ 0.1% of the energy from the electron beam to produce population inversions. The small-collision cross sections for relativistic electrons act as the primary limitation to the transfer of more energy to the gas molecules. Dependence of the laser energy on isotopes and temperature indicates that the spectral linewidth is due to Doppler broadening, and consequently higher power and optical gain are available by cooling the gases to ∼ 90 K or lower. The additional optical gain allows lasing to be observed at shorter wavelengths (1098 Å as compared to 1161 Å) and at higher powers near 1200 Å (∼ 5 kW/ cm2 as compared to 0.5 kW/cm2) than reported previously.