  We study the instability of solutions to the relativistic Vlasov-Maxwell
systems in two limiting regimes: the classical limit when the speed of light
tends to infinity and the quasineutral limit when the Debye length tends to
zero. First, in the classical limit $\varepsilon \to 0$, with $\varepsilon$
being the inverse of the speed of light, we construct a family of solutions
that converge initially polynomially fast to a homogeneous solution $\mu$ of
Vlasov-Poisson in arbitrarily high Sobolev norms, but become of order one away
from $\mu$ in arbitrary negative Sobolev norms within time of order $|\log
\varepsilon|$. Second, we deduce the invalidity of the quasineutral limit in
$L^2$ in arbitrarily short time.
