  We investigate the effect of strong magnetic fields on the adiabatic radial
oscillations of hadronic stars. We describe magnetized hadronic matter within
the framework of the relativistic nonlinear Walecka model and integrate the
equations of relativistic radial oscillations to determine the fundamental
pulsation mode. We consider that the magnetic field increases, in a density
dependent way, from the surface, where it has a typical magnetar value of
$10^{15}$ G, to the interior of the star where it can be as large as $3 \times
10^{18}$ G. We show that magnetic fields of the order of $10^{18}$ G at the
stellar core produce a significant change in the frequency of neutron star
pulsations with respect to unmagnetized objects. If radial pulsations are
excited in magnetar flares, they can leave an imprint in the flare lightcurves
and open a new window for the study of highly magnetized ultradense matter.

High Energy Astrophysical Phenomena;High Energy Physics - Phenomenology;Nuclear Theory