  We study the eigenvalues of time-harmonic Maxwell's equations in a cavity
upon changes in the electric permittivity $\varepsilon$ of the medium. We prove
that all the eigenvalues, both simple and multiple, are locally Lipschitz
continuous with respect to $\varepsilon$. Next, we show that simple eigenvalues
and the symmetric functions of multiple eigenvalues depend real analytically
upon $\varepsilon$ and we provide an explicit formula for their derivative in
$\varepsilon$. As an application of these results, we show that for a generic
permittivity all the Maxwell eigenvalues are simple.
