Abstract We describe a Herschel Space Observatory 194–671 μ m spectroscopic survey of a sample of 121 local luminous infrared galaxies and report the fluxes of the CO J to J –1 rotational transitions for , the N ii 205 μ m line, the C i lines at 609 and 370 μ m, as well as additional and usually fainter lines. The CO spectral line energy distributions (SLEDs) presented here are consistent with our earlier work, which was based on a smaller sample, that calls for two distinct molecular gas components in general: (i) a cold component, which emits CO lines primarily at J  ≲ 4 and likely represents the same gas phase traced by CO (1−0), and (ii) a warm component, which dominates over the mid- J regime (4 <  J  ≲ 10) and is intimately related to current star formation. We present evidence that the CO line emission associated with an active galactic nucleus is significant only at J  > 10. The flux ratios of the two C i lines imply modest excitation temperatures of 15–30 K; the C i 370 μ m line scales more linearly in flux with CO (4−3) than with CO (7−6). These findings suggest that the C i emission is predominantly associated with the gas component defined in (i) above. Our analysis of the stacked spectra in different far-infrared (FIR) color bins reveals an evolution of the SLED of the rotational transitions of vapor as a function of the FIR color in a direction consistent with infrared photon pumping.