In [6] and [7] the author introduces the notion of filiform Lie superalgebras, generalizing the filiform Lie algebras studied by Vergne in the sixties. In these appers, the superalgebras whose even part is isomorphic to the model filiform Lie algebra L n are studied and classified in low dimensions. Here we consider a class of superalgebras whose even part is the filiform, naturally graded Lie algebra Q n , which only exists in even dimension as a consequence of the centralizer property. Certain central extensions of Q n which preserve both the nilindex and the cited property are also generalized to obtain nonfiliform Lie superalgebras.