Many physical and man-made systems have hidden time-scales characterized by two singular perturbation parameters. This form often arises for nonlinear dynamic networks due to the presence of small and large storage elements, such as capacitors, material and energy reservoirs, masses etc., interconnected with small and large resistors, weak and strong springs, admittances etc. In this paper we emphasize the physical situation by examples and also present a manifold-based analysis which permits the construction of a nonsingular transformation for expressing the original problem in an explicit form. The interpretation of these hidden time-scales is based on aggregate conservation and hierarchical equilibrium properties, a refinement of those presented previously.
