  We present near-infrared spectroscopy for a complete sample of 33
ultraluminous infrared galaxies at a resolution of R\approx 1000. Most of the
wavelength range from 1.80-2.20 microns in the rest frame is covered, including
the Pa-alpha and Br-gamma hydrogen recombination lines, and the molecular
hydrogen vibration-rotation 1-0 S(1) and S(3) lines. Other species, such as He
I, [Fe II], and [Si VI] appear in the spectra as well, in addition to a number
of weaker molecular hydrogen lines. Nuclear extractions for each of the
individual galaxies are presented here, along with spectra of secondary nuclei,
where available. The Pa-alpha emission is seen to be highly concentrated on the
nuclei, typically with very little emision extending beyond a radius of 1 kpc.
Signatures of active nuclei are rare in the present sample, occurring in only
two of the 33 galaxies. It is found that visual extinctions to the nuclei via
the Pa-alpha/Br-gamma line ratio in excess of 10 magnitudes are relatively
common among ULIRGs, and that visual extinctions greater than 25 mag are
necessary to conceal a QSO emitting half the total bolometric luminosity. The
vibration-rotation lines of molecular hydrogen appear to be predominantly
thermal in origin, with effective temperatures generally around 2200 K. The
relative nuclear velocities between double nucleus ULIRGs are investigated,
through which it is inferred that the maximum deprojected velocity difference
is about 200 km/s. This figure is lower than the velocities predicted by
physical models of strong interactions/mergers of large, gas-rich galaxies.
