  Let $N_{k} (\g)$ be a vertex operator algebra (VOA) associated to the
generalized Verma module for affine Lie algebra of type $A_{\ell -1} ^{(1)}$ or
$C_{\ell} ^{(1)}$. We construct a family of ideals $J_{m,n} (\g)$ in $N_{k}
(\g)$, and a family $V_{m,n} (\g)$ of quotient VOAs. These families include
VOAs associated to the integrable representations, and VOAs associated to
admissible representations at half-integer levels investigated in
q-alg/9502015. We also explicitly identify the Zhu's algebras $A(V_{m,n} (\g))$
and find a connection between these Zhu's algebras and Weyl algebras.
