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A method of designing two-dimensional recursive digital filters is to employ wave digital filter techniques on two-variable analog networks possessing the desired frequency response characteristics. In this paper a study is initiated on the structures of singly terminated and doubly terminated 2-variable lossless ladder networks which are often the starting points in the design of wave digital filters. It is shown that transfer functions of singly terminated ladder networks possess second kind singularities. A class of doubly terminated cascade ladder networks whose transfer functions are free of second kind singularities is identified and their properties studied. The necessary and sufficient condition that a given rational function has to satisfy so that it can be realized as the voltage transfer function of a network belonging to the above class is obtained. A procedure to design such networks from a given transfer function is also described.