The predicted effects associated with the resonances that occur in a multiple scattering theory of electron diffraction by crystals 2) are (a) a peak in the 00 beam intensity at an electron energy below that of the lowest-energy resonance, and (b) minima in all beam intensities at the energy of each resonance. According to the theory for crystals made up of identical atom layers, with one atom per unit mesh in each layer, there is a resonance associated with the emergence of each diffracted beam parallel to the surface. The theory is extended to the case of two atoms per unit mesh in each layer. In specific applications to alkali halide (001) and graphite (0001) surfaces, it is shown that the theory leads to the same result as for the case of one atom per unit mesh-layer, except in that for alkali halides there is no resonance associated with the emergence of beams whose index sum is odd. The theory indicates that both the energy interval between the resonance and the emergence energy of the associated beam, and the energy interval between the resonance peak and the resonance, are approximately independent of beam orientation. It is proposed that an identification of resonance effects can be based on these properties. Sets of experimental 00 reflectivity curves, showing the effects of varying the primary beam orientation, are presented for NaF and graphite crystals. In each set of curves, and in the corresponding sets for LiF crystal 4), series of resonance peaks are identified on the basis of a correlation with the emergence energies of the relevant diffracted beams. It is shown that in the case of LiF crystal the resonance minimum in the 00 intensity, associated with the emergence of the 1̄1̄ beam, may be displayed by defocussing the diffraction pattern. The display consists of a dark line that crosses the 00 spot. In experiments at different angles of incidence, the energy at which the line crosses the spot center differs by a fixed amount from the 1̄1̄ emergence energy. The observation is explained in detail on the basis of the resonance mechanism. The resonance minimum is displayed in another way in multiple exposure photographs of the diffraction pattern of a stress-annealed pyrolytic (rotationally disordered) graphite sample in which successive exposures correspond to small increments in the angle of incidence. The photographs are criss-crossed by dark lines, which is identified with the loci of resonance conditions. The observation of resonance effects is interpreted as evidence for long-range dynamical interactions involving ≳ 10 4 atoms per atom layer in the crystal.