  We classify integrable irreducible highest weight representations of
non-twisted affine Lie superalgebras. We give a free field construction in the
level~1 case. The analysis of this construction shows, in particular, that in
the simplest case of the $s\ell (2|1)$ level~1 affine superalgebra the
characters are expressed in terms of the Appell elliptic function. Our results
demonstrate that the representation theory of affine Lie superalgebras is quite
different from that of affine Lie algebras.
