  We discuss the general conditions ensuring relativistic causality in an
effective theory based on the derivative expansion. Relativistic causality
implies that the Green function vanishes in the space-like region. It is known
that a naive derivative expansion violates causality in some cases such as the
first-order relativistic dissipative hydrodynamics. We note that the Lorentz
covariance, and the equal order of time and space derivatives do not ensure
causality. We derive the general conditions for causality that should be
satisfied by any effective theories respecting special relativity. The
conditions are the followings: (i) the imaginary part of poles of the Green
function is bounded at the large momentum limit, (ii) the front velocity is
smaller than the speed of light, and (iii) the coefficient of the highest-order
time derivative does not include space derivatives.
