DC magnetoresistive effects were observed in above-percolation-threshold loaded Fe-filled carbon nanotube/polyurethane-urea composite samples. A phenomenological model is derived from interpretation of resistance relaxation for a range of axial strains. The large instantaneous magnetoresistance of + 90% observed at low axial strain was a result of conduction pathway breaking caused by preferential orientation of the conducting nanotubes perpendicular to the axial current flow: a result of the magnetic torque experienced by the ferromagnetic nanotube core. At large strain the observed large instantaneous change in resistance of - 90% resulted from voltage-driven relaxation in the conducting nanotube network. At high axial strain the competition between voltage-driven relaxation and a magnetic torque gave rise to an oscillatory component of resistance relaxation.