This report describes a new approach to nonlinear RLC-networks which is based on the fact that the system of differential equations for such networks has the special form
\[
L
(
i
)
d
i
d
t
=
∂
P
(
i
,
v
)
∂
i
,
C
(
v
)
d
v
d
t
=
−
∂
P
(
i
,
v
)
∂
v
.
L\left ( i \right )\frac {{di}}{{dt}} = \frac {{\partial P\left ( {i,v} \right )}}{{\partial i}},C\left ( v \right )\frac {{dv}}{{dt}} = - \frac {{\partial P\left ( {i,v} \right )}}{{\partial v}}.
\]
The function,
P
(
i
,
v
)
P\left ( {i,v} \right )
, called the mixed potential function, can be used to construct Liapounov-type functions to prove stability under certain conditions. Several theorems on the stability of circuits are derived and examples are given to illustrate the results. A procedure is given to construct the mixed potential function directly from the circuit. The concepts of a complete set of mixed variables and a complete circuit are defined.