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In this paper, we study two-fluid compressible Euler-Maxwell equations in the whole space or periodic space. In comparison with the one-fluid case, we need to deal with the difficulty mainly caused by the nonlinear coupling and cancelation between electrons and ions. Precisely, the expected dissipation rates of densities for two carriers are no longer available. To capture the weaker dissipation, we develop a continuity for compositions, which is a natural generalization from Besov spaces to Chemin-Lerner spaces (space-time Besov spaces). An elementary fact that indicates the relation between homogeneous Chemin-Lerner spaces and inhomogeneous Chemin-Lerner spaces will been also used.

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