YBa2Cu3O7−&dgr;films grown on rolling-assisted biaxially textured substrates carry critical current densities105–106A/cm2at 77 K and low applied magnetic fields. In the low-field and low-current regime, ac transport current studies show hysteresis energy loss (per cycle and per unit length) roughly the value expected for a superconductor of elliptic cross section. The critical currentIcwas deduced from observed dc and dynamic current-voltage relations. The power loss rises sharply asI0(the maximum current in each cycle) is raised aboveIc.In the present configuration, ferromagnetic hysteresis of the Ni substrate contributes little or no loss. ©1997 American Institute of Physics.