We have studied the properties of superconducting strip lines, based on epitaxial YBCO thin films, at high current densities. Experiments performed with short constant current pulses show that a quasi spontaneous highly dissipative state (HDS) appears at high current densities. By carefully measuring the temperature of the YBCO line, we found that its temperature is still below T/sub c/ when the HDS occurs, indicating that this state does not originate from a thermal runaway. Once initiated, this HDS starts to propagate with an initial velocity larger than 100 m/s, which is one order of magnitude higher than thermal velocities. We also applied constant voltage pulses to the YBCO line, therefore simulating a real short circuit. We found that the spatial extent of the HDS along the line, a few microseconds after the short circuit, depends linearly on the applied voltage. These results allow explanation of the fast switching properties observed in superconducting fault current limiters (SFCL) and the fact that the peak current is limited at, typically, 3 times the critical current.