  For a nondegenerate additive subgroup $G$ of the $n$-dimensional vector space
$F^n$ over an algebraically closed field $F$ of characteristic zero, there is
an associative algebra and a Lie algebra of Weyl type $W(G,n)$ spanned by all
differential operators $u D_1^{m_1}... D_n^{m_n}$ for $u\in F[G]$ (the group
algebra), and $m_1,...,m_n \ge 0$, where $D_1, ...,D_n$ are degree operators.
In this paper, it is proved that an irreducible quasifinite $W(\Z,1)$-module is
either a highest or lowest weight module or else a module of the intermediate
series; furthermore, a classification of uniformly bounded $W(\Z,1)$-modules is
completely given. It is also proved that an irreducible quasifinite
$W(G,n)$-module is a module of the intermediate series and a complete
classification of quasifinite $W(G,n)$-modules is also given, if $G$ is not
isomorphic to $\Z$.
