  We incorporate non-thermal excitation and ionization processes arising from
non-thermal electrons that result from \gamma-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 (1992). We applied the non-thermal calculations to the blue supergiant
explosion model whose early evolution was studied in Dessart & Hillier (2010).
Non-thermal processes generally increase excitation and ionization and decrease
the temperature of the ejecta. We confirm that non-thermal processes are
crucial for modeling the nebular spectra. Both optical HI and HeI lines are
significantly strengthened. While optical HeI lines are not easily discerned in
observational spectra due to severe blending with other lines, HeI 2.058 \mu m
provides an excellent opportunity to infer the influence of non-thermal
processes. We also discuss the processes controlling the formation of the HeI
lines during the nebular epoch. Most lines of other species are only slightly
affected. We also show that the inclusion of FeI has substantial
line-blanketing effects on the 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 H\alpha. 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 a supernova
ejecta, whatever the type and the epoch.
