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When two circuits such as filters or transmission lines are coupled together by means of distributed reactances which can vary sinusoidally in time and space, energy can be converted between waves of different frequencies in a variety of ways. If the waves on the two transmission lines are characterized by frequencies ω1 and ω2 and phase constants β1 and β2, while the coupling reactances vary as ω=ω1−ω2 and β=β1−β2+Δβ, power P1 at ω1 is converted into power P2 at ω2 and vice versa in a manner reminiscent of waves on coupled passive circuits, except that a relationship (P2/ω2)=(P1/ω1) is obeyed. If the group velocities on both transmission lines are in the same direction, the direction of power transfer reverses periodically with distance. If they are not in the same direction, the power transfer increases monotonically with distance for small Δβ but reverses periodically for Δβ larger than a certain limit. When the coupling reactance varies as given by ω=ω1+ω2 and β=β1+β2, parametric amplification is possible in the form of exponentially growing waves at frequencies ω1 and ω2 if the group velocities are in the same direction, and in a form reminiscent of the backward wave amplifier when the group velocities are not in the same direction. In both cases the excess energy is supplied by the variable coupling reactance and can be indefinitely large. Possible applications of new principles of these coupled circuits to broad-band frequency converters, frequency-channel selectors, wide-band amplifiers, tunable narrow-band amplifiers, and oscillators are described. Noise performances of the circuits are also discussed.