  In this paper, we study the well-posedness in critical Besov spaces for
two-fluid Euler-Maxwell equations, which is different from the one fluid case.
We need to deal with the difficulties mainly caused by the nonlinear coupling
and cancelation between two carriers. Precisely, we first obtain the local
existence and blow-up criterion of classical solutions to the Cauchy problem
and periodic problem pertaining to data in Besov spaces with critical
regularity. Furthermore, we construct the global existence of classical
solutions with aid of a different energy estimate (in comparison with the
one-fluid case) provided the initial data is small under certain norms.
Finally, we establish the large-time asymptotic behavior of global solutions
near equilibrium in Besov spaces with relatively lower regularity.
