The IA-automorphism group IAn of the free group Fn is a normal subgroup of the automorphism group of Fn, which is an analogue of the Torelli groups of surfaces. The general linear group GL(n,Z) acts on the rational (co)homology of IAn. We study the GL(n,Z)-module structure of the rational (co)homology of IAn for sufficiently large n. We also consider the stable rational (co)homology of the Torelli groups of surfaces. This talk is partly based on joint work with Kazuo Habiro.