  When we describe string propagation on non-compact or singular Calabi-Yau
manifolds by CFT, continuous as well as discrete representations appear in the
theory. These representations mix in an intricate way under the modular
transformations. In this article, we propose a method of combining discrete and
continuous representations so that the resulting combinations have a simpler
modular behavior and can be used as conformal blocks of the theory. We compute
elliptic genera of ALE spaces and obtain results which agree with those
suggested from the decompactification of K3 surface. Consistency of our
approach is assured by some remarkable identity of theta functions.
  We include in the appendix some new materials on the representation theory of
${\cal N}=4$ superconformal algebra.
