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The current limiting properties of textured and epitaxial YBa2Cu307 films with different thickness on various substrates (i.e. r-cut sapphire, polycrystalline Al2O3 and Y-stabilized ZrO2) are examined. The correlation between structural, morphological, superconducting properties and the evailution of current and electrical field during dc and ac current pulses are determined. The best results are obtained in epitaxial YBa2Cu3O7 films on large-area CeO2/sapphire with a thin Au-top layer. They are characterized by Tc(ind)=88-90K, ΔTc(ind)=O.5K, Jc(77K,res.)=2-3.7MA/cm2 and FWHM(005) = 0.2°. During voltage pulse measurements the highest values for the dissipated power Pmax/A=2.6MW/m2, voltage Umax/l= 10.9 V/cm, and Rmax/Ro=2.33 and the highest mean temperature of the film of Tmax=650-700K could be obtained. The maximum current of (2-6)Ic was reached after ∼4μsec and within lmsec the current was reduced to values below Ic2Cu3O7 on polycrystalline Al2O3 and YSZ are Tc,off(ind)=87K, ΔTc=2K, Jc(77K)= 0.2MA/cm2 and FWHM(005)=0.9° yielding Pmax/A=O.7MW/m2, Umax/l=6.5 V/cm, Rmax/Ro=1.4 (Tmax≈500K) and reaction times of ∼10msec.