Based on far-infrared spectroscopy of a small sample of nearby infrared-bright and ultraluminous infrared galaxies (ULIRGs) with the ISO Long Wavelength Spectrometer, we find a dramatic progression in ionic/atomic fine-structure emission line and molecular/atomic absorption line characteristics in these galaxies extending from strong [O III]52,88 and [N III]57 micron line emission to detection of only faint [C II]158 micron line emission from gas in photodissociation regions in the ULIRGs. The molecular absorption spectra show varying excitation as well, extending from galaxies in which the molecular population mainly occupies the ground state to galaxies in which there is significant population in higher levels. In the case of the prototypical ULIRG, the merger galaxy Arp 220, the spectrum is dominated by absorption lines of OH, H2O, CH, and [O I]. Low [O III]88 micron line flux relative to the integrated far-infrared flux correlates with low excitation and does not appear to be due to far-infrared extinction or to density effects. A progression toward soft radiation fields or very dusty HII regions may explain these effects.