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The experimental evidence presented confirms the existence of a statistical nature in the laser-induced intrinsic damage process both in the bulk and on the surfaces of transparent materials. A damage process determined by an electron-avalanche breakdown with statistical starting properties was found to be consistent with the data. The importance of irradiating only a small volume of the material in order to avoid studying inclusion-induced laser damage is discussed. In addition, a new procedure was developed to permit rapid identification of the occurrence of damage due to an intrinsic process.