  Rao and Zhao classified the irreducible integrable modules with finite
dimensional weight spaces for the untwisted affine superalgebras which are not
$\hat{A}(m,n)$ ($m\ne n$) or $\hat{C}(m)$. Here we treat the latter affine
superalgebras to complete the classification. The problem boils down to
classifying the irreducible zero-level integrable modules with finite
dimensional weight spaces for these affine superalgebras, which is solved in
this paper. We note in particular that such modules for $\hat{A}(m,n)$ ($m\ne
n$) and $\hat{C}(m)$ must be of highest weight type, but are not necessarily
loop modules. This is in sharp contrast to the cases of ordinary affine
algebras and the other types of affine superalgebras.
