  In solar EUV spectra the He I and He II resonance lines show unusual
behaviour and have anomalously high intensities compared with other transition
region lines. The formation of the helium resonance lines is investigated
through extensive non-LTE radiative transfer calculations. The model
atmospheres of Vernazza, Avrett & Loeser are found to provide reasonable
matches to the helium resonance line intensities but significantly
over-estimate the intensities of other transition region lines. New model
atmospheres have been developed from emission measure distributions derived by
Macpherson & Jordan, which are consistent with SOHO observations of transition
region lines other than those of helium. These models fail to reproduce the
observed helium resonance line intensities by significant factors. The
possibility that non-Maxwellian electron distributions in the transition region
might lead to increased collisional excitation rates in the helium lines is
studied. Collisional excitation and ionization rates are re-computed for
distribution functions with power law suprathermal tails which may form by the
transport of fast electrons from high temperature regions. Enhancements of the
helium resonance line intensities are found, but many of the predictions of the
models regarding line ratios are inconsistent with observations. These results
suggest that any such departures from Maxwellian electron distributions are not
responsible for the helium resonance line intensities.
