We incorporate non-thermal excitation and ionization processes arising from non-thermal electrons that result from γ-ray energy deposition into our radiative transfer code cmfgen. The non-thermal electron distribution is obtained by solving the Spencer–Fano equation using the procedure of Kozma & Fransson. We applied the non-thermal calculations to the blue supergiant explosion model whose early evolution was studied in Dessart & Hillier. Non-thermal processes generally increase excitation and ionization and decrease the temperature of the ejecta. We confirm that non-thermal processes are crucial for modelling nebular spectra. Both optical H i and He i lines are significantly strengthened. While optical He i lines are not easily discerned in observational spectra due to severe blending with other lines, He i 2.058 μm provides an excellent opportunity to infer the influence of non-thermal processes. We also discuss the processes controlling the formation of He i lines during nebular epochs. Most lines of other species are only slightly affected. We also show that the inclusion of Fe i has substantial line-blanketing effects on optical spectra. Our model spectra and synthetic light curves are compared to the observations of SN 1987A. The spectral evolution shows broad agreement with the observations, especially Hα. The uncertainties of the non-thermal solver are studied, and are expected to be small. With this new addition of non-thermal effects in cmfgen, we now treat all known important processes controlling the radiative transfer of supernova ejecta, whatever the type and the epoch.