  We extend to the category of crossed modules of Leibniz algebras the notion
of biderivation via the action of a Leibniz algebra. This results into a pair
of Leibniz algebras which allow us to construct an object which is the actor
under certain circumstances. Additionally, we give a description of an action
in the category of crossed modules of Leibniz algebras in terms of equations.
Finally, we check that, under the aforementioned conditions, the kernel of the
canonical map from a crossed module to its actor coincides with the center and
we introduce the notions of crossed module of inner and outer biderivations.
