  In this paper, we study the representation theory for the affine Lie algebra
$\H$ associated to the Nappi-Witten model $H_{4}$. We classify all the
irreducible highest weight modules of $\H$. Furthermore, we give a necessary
and sufficient condition for each $\H$-(generalized) Verma module to be
irreducible. For reducible ones, we characterize all the linearly independent
singular vectors. Finally, we construct Wakimoto type modules for these Lie
algebras and interpret this construction in terms of vertex operator algebras
and their modules.
