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This paper presents an extension to the popular nodal and modified nodal formulation methods that allows elements whose characteristic functions include controlling variables, in addition to voltages and currents, other variables, such as charge, flux, and other physical parameters, to be included in the circuit equation formulation in a straightforward manner. Stamps, similar to nodal and modified nodal circuit element stamps, are developed to include these elements in the circuit matrix equation without the need of deriving equivalent circuit models consisting of interconnections of elements characterized only by currents and voltages, as in the current practice. The method is applied to derive circuit stamps of memristive, memcapacitive, meminductive, and other complex device models. The method reduces the size of the overall circuit matrix and allows easy model evaluation and linearization during the circuit iterative solution process.