Abstract: The method of synthesizing multiterminal switching circuits described in this paper is an improvement on Roginsky’s work. A basic set of numbers characterihing the circuit states is defined and a method for designing series-parallel switching circuits is given. With the consideration of the sneaking circuits, the general set of numbers of circuit states and sneaking set of numbers of circuit states are defined. By using these sets of numbers, circuits can be further simplified, and it is even possible to obtain circuits of the bridge type.