A theory is developed that shows the effect of cross-relaxation processes on the operation of a single-frequency gas laser oscillator. The influence of one type of cross relaxation, that due to radiation trapping, is shown to depend not only on the diameter of the gas discharge tube, but also on the diameter of the laser beam. The theory is used to calculate the saturation parameter for the 6328-Å He:Ne laser line using values of the cross-relaxation rate found from previous measurements of the cross-relaxation parameter. The calculated values are in good agreement with earlier experimental measurements. The theory is also used to compute values of the two decay rates used to fit Lamb-dip measurements, and very good agreement is obtained with the Lamb-dip results reported by Dietel.