In this paper, we investigate the behaviour of the Serre spectral sequence
with respect to the algebraic structures of string topology in generalized
homology theories, specificially with the Chas-Sullivan product and the
corresponding coproduct and the module structures. We prove compatibility for
two kinds of fibre bundles: the fibre bundle $\Omega^n M \to L^n M \to M$ for
an h_*-oriented manifold M and the looped fibre bundle $L^n F \to L^n E \to L^n
B$ of a fibre bunde $F \to E \to B$ of h_*-oriented manifolds.