A design for a superconducting niobium slow-wave accelerating structure has been explored that may have performance and cost advantages over existing technology. The option considered is an array of pairs of quarter-wave coaxial-line resonant cavities, the two elements of each pair strongly coupled through a short superconducting transmission line. In the linac formed by such an array, each paired structure is independently phased. A disadvantage of two-gap slow wave structures is that each cavity is relatively short, so that a large number of independently-phased elements is required for a linac. Increasing the number of drift tubes per cavity reduces the number of independently-phased elements but at the cost of reducing the range of useful velocity acceptance for each element. Coupling two cavities splits the accelerating rf eigenmode into two resonant modes each of which covers a portion of the full velocity acceptance range of the original, single cavity mode. Using both of these resonant modes makes feasible the use of coupled cavity pairs for a linac with little loss in velocity acceptance. (Author) 2 figs., 8 refs.