Let π€ be an n-Lie superalgebra. We study the double derivation algebra [Formula: see text] and describe the relation between [Formula: see text] and the usual derivation Lie superalgebra Der(π€). We show that the set [Formula: see text] of all double derivations is a subalgebra of the general linear Lie superalgebra gl(π€) and the inner derivation algebra ad(π€) is an ideal of [Formula: see text]. We also show that if π€ is a perfect n-Lie superalgebra with certain constraints on the base field, then the centralizer of ad(π€) in [Formula: see text] is trivial. Finally, we give that for every perfect n-Lie superalgebra π€, the triple derivations of the derivation algebra Der(π€) are exactly the derivations of Der(π€).