  This paper investigates the effect of collisional enhancement of the hydrogen
lines on the derivation of the helium abundances in low metallicity H II
regions. For this, we have constructed a grid of photoionization models
relevant for the analysis of giant \hii regions in blue compact galaxies. We
show that the effect of collisional excitation on the Halpha/Hbeta ratio can be
quite important (up to 8% or more). The impact of this effect on the
determination of the helium mass fraction has been tracked on four
low-metallicity blue compact galaxies for which Keck spectra are available and
which are among the best objects for the quest of the pregalactic helium
abundance. We find that taking into account the effects of collisional
excitation of hydrogen results in an upward correction of the helium mass
fraction Y by up to 5%. However, combining with other systematic effects
usually not considered in the determination of the helium abundance in
low-metallicity galaxies, the resulting uncertainty should be much less.
