  In this paper we study the following nonlinear Maxwell's equations \\
$\varepsilon \E_{t}+\sigma(x,|\E|)\E= \g \vh +\F,\, \vh_{t}+\g \E=0$, where
$\sigma(x,s)$ is a monotone graph of $s$. It is shown that the system has a
unique weak solution. Moreover, the limit of the solution as
$\varepsilon\rightarrow 0$ converges to the solution of quasi-stationary
Maxwell's equations.
