  Irreducible nonzero level modules with finite-dimensional weight spaces are
studied for non-twisted affine Lie superalgebras. A complete classification is
obtained for superalgebras A(m,n)^ and C(n)^. In other cases the classification
problem is reduced to the classification of cuspidal modules over
finite-dimensional cuspidal Lie superalgebras described by Dimitrov, Mathieu
and Penkov. It is also shown that any irreducible weakly integrable (in the
sense of Kac and Wakimoto) module is highest weight.
