Let $\pi _1: W \to V$ and $\pi _{2} : V \to S$ be holomorphic submersions of complex varieties with compact fibre. Let $\xi $ be a holomorphic vector bundle on $W$. We prove the functoriality of the analytic torsion forms with respect to the composition of two submersions. This result extends to a relative situation a result by Berthomieu-Bismut, proved in the case where $S$ is a point.