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A multilayer RC distributed network is a -port consisting of alternately sandwiched layers of dielectric and resistive materials of uniform width and thickness. The immittance functions of such a network admit canonical forms that lead to equivalent networks consisting of decoupled uniform RC lines. Necessary and sufficient conditions are given for a transcendental frequency function to be a network function of a multilayer RC distributed network. The coefficients of the voltage transfer function form a sequence whose sign variation is important in the synthesis.