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We discuss the general conditions ensuring relativistic causality in aneffective theory based on the derivative expansion. Relativistic causalityimplies that the Green function vanishes in the space-like region. It is knownthat a naive derivative expansion violates causality in some cases such as thefirst-order relativistic dissipative hydrodynamics. We note that the Lorentzcovariance, and the equal order of time and space derivatives do not ensurecausality. We derive the general conditions for causality that should besatisfied by any effective theories respecting special relativity. Theconditions are the followings: (i) the imaginary part of poles of the Greenfunction is bounded at the large momentum limit, (ii) the front velocity issmaller than the speed of light, and (iii) the coefficient of the highest-ordertime derivative does not include space derivatives.

General conditions ensuring relativistic causality in an effective field theory based on the derivative expansion