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X-ray radiation damage of a lysozyme single crystal by an intense monochromatic beam from a third-generation radiation source at the Advanced Photon Source has been studied. The results show that primary radiation damage is linearly dependent on the X-ray dose even when the crystal is at cryogenic temperatures. The existence of an upper limit for the primary radiation damage was observed. Above the threshold of approximately 1 × 107 Gy, excessive damage of the crystal develops which is interpreted as the onset of secondary and/or tertiary radiation damage. This upper limit of X-ray dose is compared with Henderson's limit [Henderson (1990). Proc. R. Soc. London, B241, 6-8], and its implication for the amount of useful X-ray diffraction data that can be obtained for crystals of a given scattering power is also discussed.