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Characteristics of a gas laser amplifier are theoretically analyzed by employing Lamb's model. A wave equation in the time domain is obtained when traveling waves in the positive and negative directions are present simultaneously in the nonlinear active medium. The wave equation which contains linear and third-order nonlinear terms is applicable to any spectral construction of the incident signal, such as discrete, continuous, and mixed. An approximate solution of the wave equation is obtained in the frequency domain. Some characteristics of a kernel which appears in the frequency-domain representation are discussed. As an application of the theory, characteristics of one- and two-frequency amplifiers are calculated and compared to previous analysis.