High-resolution transmission electron microscopy (HRTEM), electron diffraction, and electron energy-loss spectroscopy (EELS) were used to characterize electron-beam-induced structural transformations in crystalline samples of C60 and C70. During these transformations, the electron-diffraction patterns became progressively more diffuse, with the outer diffraction spots disappearing first, followed in succession by the disappearance of the inner spots. We interpret this course of evolution in the diffraction patterns as evidence of degradation of the crystalline structure via the destruction of individual molecules, as opposed to electron-beam-induced motion of intact fullerene molecules. EELS analyses of the data indicate that the final state of these transformations was amorphous carbon.