In most cases, astrophysical plasmas are modelled using Maxwellian velocity distributions, even under NEI or PIE conditions. Often this is justified, but there are situations where deviations from a Maxwellian distribution occur. Examples are accelerated electrons penetrating cooler regions, as may occur in or near shocks or flares. We refrain here from a full discussion, but only mention here that spectral codes such as SPEX (Sect. 10.1) allow the calculation of the ionisation balance and the emanating spectrum under such circumstances, provided the true electron distribution can be approximated by the sum of non-relativistic Maxwellians. When there are strong relativistic electron contributions, this approach cannot be used anymore as here relativistic corrections to the cross sections are needed, which are usually not taken into account in most plasma codes.