Abstract Measured intensities of diffraction spots from multilayers were unchanged or even often increased at initial exposures before subsequent exponential decrease with increasing exposure. Those phenomena result in the increase of the extinction dose with number of layers. The extinction dose which was about 1 electron/[Aring] 2 for monolayers reached the maximum value of about 14 electrons/[Aring] 2 at 12 layers. The rate of broadening of the diffraction spots was independent of specimen thickness. This result leads to the conclusion that the specimen is always being destroyed at the same rate.