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Traveling wave type parametric amplifiers have been proposed which utilize transmission lines having reactance varied by a propagating wave. An analysis indicates that in systems with little or no dispersion, pumping will not result in exponential gain of an applied signal but in a conversion of energy to a multiplicity of cross-product frequencies. Two physical models of such wide-band systems are discussed and the special case of a zero-dispersion line is analyzed. The results indicate that although the total energy increases exponentially with distance, the wave becomes extremely rich in high frequencies. Although such systems would not be useful as amplifiers, use as frequency converters is suggested.