We consider two different general problems: a three body problem with one solid body, and a two body problem with two interacting solids. This can be a Sun-planet-satellite problem and a binary system of non spherical bodies respectively. We demonstrate that after adequate averaging, these problems can be reduced to non-trivial integrable problems for which we provide the complete solutions. These results should be useful for the understanding of the evolution of planetary and satellites' spin axes over long time-scales, and thus for the search of dynamical constraints on the evolution of the Solar System.