Abstract: We report measurements of the hysteretic magnetization of YBCO under superimposed transport current cycles, together with numerical simulations of magnetization and current density profiles in the corresponding parallel configuration. Field cooled (FC) and zero-field-cooled (ZFC) experiments were carried out on polycrystalline YBa2Cu3O7?x cylinders, with both the applied magnetic field and transport current in the axial direction, and the current cycled several times, around and above the dissipative threshold. As in previously reported multicomponent field configuration experiments, the magnetization is seen to collapse to a more stable state both in FC and ZFC, because of the interplay between the shielding and transport currents. The results of our numerical simulations are in good qualitative agreement with the measurements, and the competition between shielding and transport due to vortex-pinning interactions and equilibrium magnetization effects are shown to play an important role in the range of our experiments.