The He I Lα λ 584 transfer problem for gaseous nebulae is investigated. Realistic photo-ionization models of quasar clouds and planetary nebulae are combined with the Monte Carlo line transfer technique to determine both the efficiency of destruction of λ 584 by photo-ionization of hydrogen and the mean number of scatterings undergone before destruction. We find that large fractions ( 90 per cent) of the λ 584 photons are destroyed before escaping in all cases considered. Nonetheless, the He I λλ 584, 626 doublet should be present in high redshift quasars with an observed equivalent width of ∼1Å. Detection of this doublet would provide the only clear indication of the presence or absence of a low density narrow line region for objects in which optical forbidden lines have been redshifted beyond the optical window. The strength of the He I 21S-2lP 2.0 μm line is predicted to be ∼4 times stronger than is actually observed in the planetary nebulae NGC 7027. This suggests that dust is embedded in the ionized gas and causes additional destruction of λ 584. Finally, our calculations show that photo-ionization model calculations can safely assume nearly complete on-the-spot destruction of λ 584. The common assumption that the He I singlets are formed in case B conditions is examined in an appendix. © 1980 Royal Astronomical Society. Provided by the NASA Astrophysics Data System.