  Throughout the current paper, we extend the study of Zinbiel algebras to
Zinbiel superalgebras. In particular, we show that all the Zinbiel
superalgebras over an arbitrary field are nilpotent in the same way as occurs
for Zinbiel algebras. Moreover and since the most important cases of nilpotent
algebras or superalgebras are those with maximal nilpotency index, we study the
complex null-filiform Zinbiel superalgebra, i.e. the only one single generated,
proving that is unique up to isomorphism. After that, we characterise the
naturally graded filiform ones and obtain low-dimensional classifications.
