  We define an affine Jacquet functor and use it to describe the structure of
induced affine Harish-Chandra modules at noncritical levels, extending the
theorem of Kac and Kazhdan [KK] on the structure of Verma modules in the
Bernstein-Gelfand-Gelfand categories O for Kac-Moody algebras. This is combined
with a vanishing result for certain extension groups to construct a block
decomposition of the categories of affine Harish-Chandra modules of Lian and
Zuckerman [LZ]. The latter provides an extension of the works of Rocha-Caridi,
Wallach [RW] and Deodhar, Gabber, Kac [DGK] on block decompositions of BGG
categories for Kac-Moody algebras. We also prove a compatibility relation
between the affine Jacquet functor and the Kazhdan-Lusztig tensor product. A
modification of this is used to prove that the affine Harish-Chandra category
is stable under fusion tensoring with the Kazhdan-Lusztig category (a case of
our finiteness result [Y]) and will be further applied in studying translation
functors for Kac-Moody algebras, based on the fusion tensor product.
