Electron diffraction patterns from films of long-chain paraffins show the effects of secondary elastic scattering of electrons in the form of extra spots, groups of spots, arcs of circles, diffuse bands with sharp edges, and forbidden reflections in single-crystal patterns. Examples of such effects are given and analysed to demonstrate their origin in the successive diffraction of electrons from two different single-crystal regions. It is pointed out that many effects recorded in the literature on electron diffraction may be explained in the same way. The modification of the intensities in single-crystal patterns and the appearance of forbidden reflections are treated quantitatively on the basis of secondary diffraction by parallel but non-coherent regions of crystal. Expressions are derived whereby observed intensities may be corrected for secondary scattering when once the scattering efficiency of the crystal has been deduced from the observed intensities of forbidden reflections. The importance of such corrections for purposes of structure analysis is demonstrated in the comparison of two Fourier projections made from a cross-grating pattern of dicetyl (C₃₂H₆₆), one using observed intensities and the other using corrected intensities. Both show clearly the general arrangement of the molecules, but that based on corrected intensities contains much less spurious detail than the other, and gives greater accuracy and a much clearer indication of the positions of the hydrogen atoms