Electrical networks consisting of lumped linear and memoryless nonlinear elements and an arbitrary number of lossless transmission lines are considered. It is shown that a large class of such networks can be described by a system of functional-differential equations having the form

, where the state of the system at time

is represented by

, a point in the space
![C_{H}((- \\infty ,0], E^{n})](/images/tex/11249.gif)
of bounded continuous functions mapping the interval
![(-\\infty , 0]](/images/tex/11250.gif)
into

, with the compact open topology, and the function

mapping
![C_{H}(( - \\infty , 0], E^{n})](/images/tex/11251.gif)
into

is continuous and Lipschitzian. A Lyapunov functional is presented and used to obtain several theorems concerning the stability and instability of the equilibrium solution of such networks.