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A theory of a ferromagnetic traveling-wave amplifier of parametric type is presented here. Amplification of signal power in the form of growing waves is obtained in a propagating structure which is partially or totally embedded in a ferromagnetic medium. The structure, in one of its possible forms, possesses two propagating modes: one of the modes is excited by a signal at the input end, and the other is used as an idling circuit. The structure should also support a traveling wave supplied by a local oscillator which provides, through the motion of the magnetization, a time-varying coupling between the two propagating modes. The problem is essentially that of two coupled transmission lines with a time-dependent coupling coefficient. Optimum conditions for amplification are derived. A structure consisting of two pairs of parallel wires is calculated to illustrate the general principles.