Summary: The Helmholtz-Thèvenin theorem together with its dual equivalent Mayer-Norton’s one is generalized to that of \(n\)-terminal networks. The new theorem asserts that any \(n\)-terminal network can be reduced to a set of the equivalent circuits which consist of \((n-1)(n-2)/2\) impedances and \((n-1)\) active 2-terminal elements (Helmholtz-Thevenin’s or Mayer-Norton’s equivalent circuits). Their graph is the complete one, and the active elements are connected to each other so that they make a tree. The number of the possible equivalent circuits is \(n^{n-2}\) for an \(n\)-terminal network, if we do not distinguish a Helmholtz-Thèvenin’s circuit from Mayer-Norton’s one.