[For Part I see ibid. 5, 279-319 (1986; Zbl 0615.94013).] This is the second paper in which the authors investigate nonlinear networks N containing capacitor-only cutsets and/or inductor-only loops using the theory of differentiable manifolds. Let \(\delta\) equal the sum of the number of independent capacitor-only cut sets and independent inductor-only loops. The authors define a Lie group action of \(R^{\delta}\) on the state space of N and establish sufficient conditions for the network dynamics to be invariant under the Lie group action.