  In this paper we investigate pre-derivations of filiform Leibniz algebras.
Recall that the set of filiform Leibniz algebras of fixed dimension can be
decomposed into three non-intersected families. We describe the pre-derivation
of filiform Leibniz algebras for the first and second families. We found
sufficient conditions under which filiform Leibniz algebras are strongly
nilpotent. Moreover, for the first and second families, we give the description
of characteristically nilpotent algebras which are non-strongly nilpotent.
