  W. A. Moens proved that a Lie algebra is nilpotent if and only if it admits
an invertible Leibniz-derivation. In this paper we show that with the
definition of Leibniz-derivation from W. A. Moens the similar result for non
Lie Leibniz algebras is not true. Namely, we give an example of non nilpotent
Leibniz algebra which admits an invertible Leibniz-derivation. In order to
extend the results of paper W. A. Moens for Leibniz algebras we introduce a
definition of Leibniz-derivation of Leibniz algebras which agrees with
Leibniz-derivation of Lie algebras case. Further we prove that a Leibniz
algebra is nilpotent if and only if it admits an invertible Leibniz-derivation.
Moreover, the result that solvable radical of a Lie algebra is invariant with
respect to a Leibniz-derivation was extended to the case of Leibniz algebras.
