  We study the effect of superfluidity on torsional oscillations of highly
magnetised neutron stars (magnetars) with a microphysical equation of state by
means of two-dimensional, magnetohydrodynamical- elastic simulations. The
superfluid properties of the neutrons in the neutron star core are treated in a
parametric way in which we effectively decouple part of the core matter from
the oscillations. Our simulations confirm the existence of two groups of
oscillations, namely continuum oscillations that are confined to the neutron
star core and are of Alfv\'enic character, and global oscillations with
constant phase and that are of mixed magneto-elastic type. The latter might
explain the quasi-periodic oscillations observed in magnetar giant flares,
since they do not suffer from the additional damping mechanism due to phase
mixing, contrary to what happens for continuum oscillations. However, we cannot
prove rigorously that the coherent oscillations with constant phase are normal
modes. Moreover, we find no crustal shear modes for the magnetic field
strengths typical for magnetars.We provide fits to our numerical simulations
that give the oscillation frequencies as functions of magnetic field strength
and proton fraction in the core.
