Let R be a commutative Noetherian ring, a an ideal of R and N an R-module. We prove that, for every finitely generated R-module of finite projective dimension t, the elements in the support of generalized local cohomology module Hnþt a ðM;NÞ of height n are finite for all nb0. This implies that, if R is a d-dimensional local ring, then Hdþt
1 a ðM;NÞ has finite support for arbitrary R, a and N. In addition, for a non-negative integer n, we show that if M and N are arbitrary finitely generated R-modules such that the R-modules Hia ðNÞ and Hia ðM;NÞ have finite support for all i < n, then AssHn a ðM;NÞ is finite.

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