The violent giant flares of magnetars excite QPOs which persist for hundreds of seconds, as seen in the X-ray tail following the initial burst. Recent studies, based on single-fluid barotropic magnetar models, have suggested that the lower-frequency QPOs correspond to magneto-elastic oscillations of the star. The higher frequencies, however -in particular the strong 625 Hz peak -have proved harder to explain, except as high mode multipoles. In this work we study the time evolutions of nonaxisymmetric oscillations of two-fluid Newtonian magnetars with no crust. We consider models with superfluid neutrons and normal protons, and poloidal and toroidal background field configurations. We show that multi-fluid physics (composition-gradient stratification, entrainment) tends to increase Alfvén mode frequencies significantly from their values in a single-fluid barotropic model. The higher-frequency magnetar QPOs may then be naturally interpreted as Alfvén oscillations of the multi-fluid stellar core. The lower-frequency QPOs are less easily explained within our purely fluid core model, but we discuss the possibility that these are crustal modes.