We present Herschel observations of six fine-structure lines in 25 Ultraluminous Infrared Galaxies at z<0.27. The lines, [O III]52, [N III]57, [O I]63, [N II]122, [O I]145, and [C II]158, are mostly single gaussians with widths <600 km s-1 and luminosities of 10^7 - 10^9 Solar. There are deficits in the [O I]63/L_IR, [N II]/L_IR, [O I]145/L_IR, and [C II]/L_IR ratios compared to lower luminosity systems. The majority of the line deficits are consistent with dustier H II regions, but part of the [C II] deficit may arise from an additional mechanism, plausibly charged dust grains. This is consistent with some of the [C II] originating from PDRs or the ISM. We derive relations between far-IR line luminosities and both IR luminosity and star formation rate. We find that [N II] and both [O I] lines are good tracers of IR luminosity and star formation rate. In contrast, [C II] is a poor tracer of IR luminosity and star formation rate, and does not improve as a tracer of either quantity if the [C II] deficit is accounted for. The continuum luminosity densities also correlate with IR luminosity and star formation rate. We derive ranges for the gas density and ultraviolet radiation intensity of 10^1 < n < 10^2.5 and 10^2.2 < G_0 < 10^3.6, respectively. These ranges depend on optical type, the importance of star formation, and merger stage. We do not find relationships between far-IR line properties and several other parameters; AGN activity, merger stage, mid-IR excitation, and SMBH mass. We conclude that these far-IR lines arise from gas heated by starlight, and that they are not strongly influenced by AGN activity.
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