  In this paper we study the large-time behavior of classical solutions to the
two-species Vlasov-Maxwell-Boltzmann system in the whole space $\R^3$. The
existence of global in time nearby Maxwellian solutions is known from [34] in
2006. However the asymptotic behavior of these solutions has been a challenging
open problem. Building on our previous work [10] on time decay for the simpler
Vlasov-Poisson-Boltzmann system, we prove that these solutions converge to the
global Maxwellian with the optimal decay rate of $O(t^{-3/2+\frac{3}{2r}})$ in
$L^2_\xi(L^r_x)$-norm for any $2\leq r\leq \infty$ if initial perturbation is
smooth enough and decays in space-velocity fast enough at infinity. Moreover,
some explicit rates for the electromagnetic field tending to zero are also
provided.
