  Some contracting or expanding stars are thought to host a large-scale
magnetic field in their radiative interior. By interacting with the
contraction-induced flows, such fields may significantly alter the rotational
history of the star. They thus constitute a promising way to address the
problem of angular momentum transport during the rapid phases of stellar
evolution. In this work, we aim at studying the interplay between flows and
magnetic fields in a contracting radiative zone. We propose a scenario that may
account for the post-main sequence evolution of solar-like stars, in which a
quasi-solid rotation can be maintained by a large-scale magnetic field during a
contraction timescale. Then, an axisymmetric instability would destroy this
large-scale structure and enables the differential rotation to set in. Such a
contraction driven instability could also be at the origin of the observed
dichotomy between strongly and weakly magnetic intermediate-mass stars.
