  This paper considers and extends spectral and scattering theory to
dissipative symmetric systems that may have zero speeds and in particular to
strictly dissipative boundary conditions for Maxwell's equations. Consider
symmetric systems $\partial_t - \sum_{j=1}^n A_j \partial_{x_j}$ in ${\mathbb
R}^n,\: n \geq 3$, $n$ odd, in a smooth connected exterior domain $\Omega :=
{\mathbb R}^n \setminus \bar{K}$. Assume that the rank of $A(\xi) = \sum_{j=
1}^n A_j \xi_j$ is constant for $\xi \not= 0.$ For maximally dissipative
boundary conditions on $\Omega :={\mathbb R}^n \setminus \bar{K}$ with bounded
open domain $K$ the solution of the boundary problem in ${\mathbb R}^{+} \times
\Omega$ is described by a contraction semigroup $V(t) = e^{t G_b},\:t \geq 0.$
Assuming coercive conditions for $G_b$ and its adjoint $G_b^*$ on the
complement of their kernels, we prove that the spectrum of $G_b$ in the open
half plane $\Re z < 0$ is formed only by isolated eigenvalues with finite
multiplicities.
