Seven very luminous galaxies were examined to determine the contribution of active nuclei to their luminosity, the nature of their stellar population, and the validity of previous measurements of their H₂ content. Spectra of the 2.3 μm bands of CO were used to measure the stellar velocity dispersion, and hence the mass in the central regions. The bolometric luminosity, ionizing continuum luminosity, CO index, and 2.2 μm luminosity were also determined. Models of young stellar populations were compared to the observed properties of the galaxies. It was found that four of the seven galaxies have properties which are inconsistent with those of stellar populations. The active nuclei of these four galaxies produce more than half the total light of the galaxies, but less than one-third of the 2.2 μm light. The galaxies containing AGN also have young stellar populations. There is no evidence for the existence of active nuclei in the other three galaxies. The stellar populations that dominate the starlight in the galaxies have a wide range of properties. Stellar populations range in age from 10 to 65 Myr. The timescale for star formation ranges from 5 Myr to 100 Myr. The local initial mass function is ruled out for one of the four galaxies for which stellar population analysis could be done. The molecular gas masses for some very luminous galaxies determined from the ¹²CO J = 1 → 0 line are in error. The previously determined molecular gas masses are larger than the dynamical masses. The I(CO)/M(H₂) conversion factor found for Milky Way giant molecular clouds is evidently not correct for some very luminous infrared galaxies.