The nonlinear properties of a power-saturated resonant medium are used to obtain amplification of millimeter-wave radiation. Experiments demonstrating this effect are performed with the 3.5-mm rotational resonance of hydrogen cyanide (HC12N15) gas. An incoming radiation spectrum consisting of a strong saturating component at 3.5 mm and weak sidebands is transmitted through a gas-filled, 34-in.-diam, 20-ft circular waveguide operated in the TE01 mode. Under certain conditions power can be transferred from the strong saturating component to the weak sidebands. A sideband gain with a maximum value of 1.5 dB is measured when the sidebands are phased for amplitude modulation and the saturating component input power is 4.8 mW. The bandwidth for this type of amplification is equal to the power-broadened linewidth. Sidebands phased for frequency modulation are always attenuated. The experimental results are in agreement with computations based on the solution of the quantum-mechanical Boltzmann equation. These computations indicate that a single sideband can also be amplified.