  The paper deals with the classification of a subclass of finite-dimensional
Zinbiel algebras: the naturally graded p-filiform Zinbiel algebras. A Zinbiel
algebra is the dual to Leibniz algebra in Koszul sense. We prove that there
exists, up to isomorphism, only one family of naturally graded p-filiform
Zinbiel algebras under hypothesis $n-p \geq 4.$
