For a nondegenerate additive subgroup G of the n-dimensional vector space Fn over an algebraically closed field F of characteristic zero, there is an associative algebra and a Lie algebra of Weyl typeWðG; nÞ spanned by all differential operators uDm1 1 ?Dmn n for uAF½G (the group algebra), and m1;y;mnX0; where D1;y;Dn are degree operators. In this paper, it is proved that an irreducible quasifinite WðZ; 1Þ-module is either a highest or lowest weight module or else a module of the intermediate series; furthermore, a classification of uniformly boundedWðZ; 1Þ-modules is completely given. It is also proved that an irreducible quasifinite WðG; nÞ-module is a module of the intermediate series and a complete classification of quasifinite WðG; nÞ-modules is also given, if G is not isomorphic to Z.