  The superfluid and superconducting core of a cold rotating neutron star is
expected to be threaded by a tremendous number of neutron quantised vortices
and proton fluxoids. Their interactions are unavoidable and may have important
astrophysical implications. In this paper, the various contributions to the
force acting on a single vortex to which fluxoids are pinned are clarified. The
general expression of the force is derived by applying the variational
multifluid formalism developed by Carter and collaborators. Pinning to fluxoids
leads to an additional Magnus type force due to proton circulation around the
vortex. Pinning in the core of a neutron star may thus have a dramatic impact
on the vortex dynamics, and therefore on the magneto-rotational evolution of
the star.
