Abstract Simple group‐theoretic concepts are used to develop a rigorous and comprehensive theory of symmetry for nonlinear multiport and multiterminal resistors which do not rely on geometrical arguments or other ad hoc techniques normally invoked in such studies. This theory unifies all forms of symmetry, including rotation, reflection and complementary symmetry, into a single framework. It also includes all known nonlinear symmetry principles as special cases. Moreover, a general method for identifying all symmetry characteristics possessed by a nonlinear multiport and multiterminal element is given. The main results of this paper: Several algorithms for synthesizing a nonlinear multiport or multiterminal element having any prescribed form of symmetry are presented. In particular, various examples are given which illustrate how these algorithms can be used to derive well‐known symmetrical nonlinear circuit modules such as push‐pull amplifiers, complementary‐symmetric amplifiers, rectifiers, modulators, etc.; A reduction algorithm is presented which allows a complicated symmetric element to be analysed by a much simpler reduced element; A general principle is derived for applying symmetry to achieve frequency separation in nonlinear communication circuits where the even harmonic components are separated from the odd harmonic components.
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