Multiple inelastic electron scattering is significant if the crystal is thick. Contributions from high-order scattering are compatible with that from single scattering if \(d / \Lambda >1\) , where d is specimen thickness and \(\Lambda \) is the inelastic electron scattering mean free path length. There are three types of multiple scattering processes. One is plural scattering of the electron by the same inelastic event, such as multiple plasmon excitation. The second type is consecutive multiple electron inelastic scattering by two or more different inelastic events, such as thermal diffuse scattering and valence loss scattering. The third is simultaneous excitation by two or more inelastic events in a single-scattering process, such as double-plasmon excitation (Spence and Spargo 1971; Ashley and Ritchie 1970), in which two plasmons are created during a single inelastic-scattering process. The first two process types are called multiple inelastic scattering, in which inelastic excitations are defined to occur consecutively. The third type is a multi-inelastic scattering process, in which inelastic excitations occur simultaneously during interaction with the same atom (for localized scattering only).