  We describe in the paper the graded centers of the derived categories of the
derived discrete algebras. In particular, we prove that if $A$ is a derived
discrete algebra, then the reduced part of the graded center of the derived
category of $A$ is nontrivial if and only if $A$ has infinite global dimension.
Moreover, we show that the nilpotent part of the graded center is controlled by
the objects for which the Auslander--Reiten translation coincides with a power
of the suspension functor.
