Merging galaxies sometimes have infrared luminosities as high as quasars. The origin of the infrared flux is controversial, but one of the most popular hypotheses is that the flux arises from dust heated by a starburst. If this is the case, the young stars should be surrounded by H II regions giving rise to recombination line flux. We present measurements of the Br gamma infrared recombination line of several merging galaxies and take several more from the literature. Our aim is to use a simple star formation model to see if the infrared recombination line fluxes and far-infrared fluxes are consistent with a starburst. We find that most of the mergers in this sample (six out of a total of eight) have infrared fluxes consistent with a simple starburst model. The starbursts are either young, or if they have evolved, there is a deficit of low-mass stars compared to stars in the solar neighborhood. There are two infrared-bright galaxies, Arp 220 and NGC 6240, that have a deficit of ionizing photons when compared to the other galaxies in this sample. These galaxies may be evolved starbursts in which an active nucleus dominates the far-infrared luminosity, but it is possible that extinction plus dust absorption of the L gamma alpha photons results in a much decreased recombination line flux from a starburst.