We report the observation of strong electron dephasing in a series of disordered Cu93Ge4Au3 thin films. A very short electron dephasing time possessing very weak temperature dependence around 6 K, followed by an upturn with further decrease in temperature below 4 K, is found. The upturn is progressively more pronounced in more disordered samples. Moreover, a ln T-dependent, but high-magnetic-field-insensitive, resistance rise persisting from above 10 K down to 30 mK is observed in the films. These results suggest a nonmagnetic dephasing process which is stronger than any known mechanism and may originate from the coupling of conduction electrons to dynamic defects.