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Daniel Han-Kwan and I have just submitted a paper entitled: “Nonlinear instability of Vlasov-Maxwell systems in the classical and quasineutral limits”, which is also available on arxiv: arXiv:1506.08537. In this paper, 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 ${\varepsilon \rightarrow 0}$, 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.