In this paper a "convection-nonequilibrium cross relaxation" theory is presented for a gas flow and chemical lasers: The experessions of gain coefficienr and saturated gain spec-trum are derived for the two-type flow models of a gas flow medium with turbulent or lami-nar flow mixture respectively. Some new gain saruration laws are obtained. The unsaturated and saturated gain are dependent on the streamwise distance. The numerical results show that the gain profiles of a saturated amplifier with Doppler-broadening presents some "anoma-lous" phenomena with a mixture of inhomogeneous and homogeneous profiles. The present theoretical results agree with the measured results