AbstractThe problem of determining the class of passive nonlinear networks with the C1internal energy function proposed by Wyatt, Chua et al., is closely related to the passive realization of nonlinear networks. This paper considers the positive‐real lemma which plays a fundamental role in the passive realization of linear networks. Here, the lemma is extended to general nonlinear networks using the property of solution in the optimal control problem. the results obtained provide an answer to the problem proposed by Wyatt, Chua et al. the positive‐real lemma for the linear case can easily be derived as a special case of the general nonlinear case. the realization problem for the nonlinear n‐port is formulated, and a fundamental property for the passive realization is shown as an extension of the linear