As an attempt in the research of nonlinear networks, the application of the polyterminal network theory is suggested in the present paper.The fundamental character of the nonlinear polyterminal networks with constant flux is considered. Two theorems about N-terminal nonlinear network are established as follows:Theorem I: The nonlinear X-terminal network is determined by a function system of N-1 independent functions, each of which contains N-1 independent variables.Theorem II: The equivalent network of the nonlinear N-terminal (N>2) networks can not be realized by the nonlinear elements, whose potentialdifference-flux characteristic is a function of a single variable; the potentialdifference-flux characteristic of the nonlinear elements in the equivalent network of the nonlinear N-terminal network is a function of many variables.