  It is proved that an irreducible quasifinite $W_\infty$-module is a highest
or lowest weight module or a module of the intermediate series; a uniformly
bounded indecomposable weight $W_\infty$-module is a module of the intermediate
series. For a nondegenerate additive subgroup $G$ of $F^n$, where $F$ is a
field of characteristic zero, there is a simple Lie or associative algebra
$W(G,n)^{(1)}$ spanned by differential operators $uD_1^{m_1}... D_n^{m_n}$ for
$u\in F[G]$ (the group algebra), and $m_i\ge0$ with $\sum_{i=1}^n m_i\ge1$,
where $D_i$ are degree operators. It is also proved that an indecomposable
quasifinite weight $W(G,n)^{(1)}$-module is a module of the intermediate series
if $G$ is not isomorphic to $Z$.
