Let (R, 픪) be a local ring, 픞 an ideal of R, and M, N be two finitely generated R-modules. We show that r = gdepth(M/픞M, N) is the least integer such that $H^r_{\frak a}(M, N)$ has infinite support. Also, we prove that the first non-Artinian generalized local cohomology module has finitely many associated primes.