We classify simple linearly compact n-Lie superalgebras with n>2 over a field
F of characteristic 0. The classification is based on a bijective
correspondence between non-abelian n-Lie superalgebras and transitive Z-graded
Lie superalgebras of the form L=\oplus_{j=-1}^{n-1} L_j, such that L_{-1}=g,
where dim L_{n-1}=1, L_{-1} and L_{n-1} generate L, and [L_j, L_{n-j-1}] =0 for
all j, thereby reducing it to the known classification of simple linearly
compact Lie superalgebras and their Z-gradings. The list consists of four
examples, one of them being the n+1-dimensional vector product n-Lie algebra,
and the remaining three infinite-dimensional n-Lie algebras.