We investigate the propagation of electromagnetic waves in resistive e± pair plasmas using a one-fluid theory derived from the relativistic two-fluid equations. When the resistivity normalized by the electron/positron inertia variable exceeds a critical value, the dispersion relation for electromagnetic waves shows that the group velocity is larger than the light speed in vacuum. However, in such a case, it also is found that the plasma parameter is less than unity: that is, the electron-positron pair medium no longer can be treated as plasma. Thus, the simple two-fluid approximation is invalid. This confirms that superluminal propagation of electromagnetic wave is forbidden in a plasma-a conclusion consistent with the relativistic principle of causality. As an alternative, we propose a new set of equations for "causal relativistic magnetohydrodynamics," which both have nonzero resistivity and yet are consistent with the causality principle. © 2008 The American Physical Society.