The quasi-steady-state conditions of the multi-atmospheric e-beam sustained Ar-Xe laser are investigated. It is observed that the duration of the stationary period depends on the e-beam current, discharge power deposition, and gas pressure. The laser efficiency can be as high as 8%. Beyond the stationary period the efficiency drops. The pulse energy with optimum efficiency depends strongly on the gas pressure. The maximum discharge efficiency of 5%-6% is at high pressure not sensitive to the input power. The best results are obtained for 4 bar with a discharge input power of 8 MW/l. The pulse duration with corresponding output energies is 12 ¿s with 10 J/l and 16 ¿s with 16 J/l for e-beam currents of 0.4 and 0.9 A/cm2, respectively. An analysis of the quasi-steady-state conditions that include the effects of electron collision mixing and atomic quenching is presented. The effects of output power saturation by the fractional ionization and atomic collisions are in agreement with the observations. The analysis clarifies the optimum performance conditions