The convection of the gain medium is a decisive factor for large increase in power output of gas lasers. The present analysis shows that both the saturation intensity and the laser power density (or the small-signal gain coefficient) by which CW laser is characterized increase nonlinearly with the flow speed and tend to the respective limiting values. It is also shown that the increment of the saturation intensity does not go beyond about 10 times, and a large increase in power density is caused by the accumulation of excited energy in the flowing gas. These results are not the same as those of the currently accepted theory which predicts that the saturation intensity increase linearly and unlimitedly with flow speed, and a large increase in power density is due to a large increase in the saturation intensity. The present quantitative results of the variation of the saturation intensity with the gas flow transient time are consistent with the experimental data of the flowing CO2 gas lasers, where the gas flow transient time denotes the time required for the flowing gas to move across the gas gain region, or the probing-beam section.