We present near-infrared spectroscopy for a complete sample of 33 ultralumi
nous infrared galaxies at a resolution of R approximate to 1000. Most of th
e wavelength range from 1.80-2.20 mum in the rest frame is covered, includi
ng the Pa alpha and Br gamma hydrogen recombination lines, and the molecula
r 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 second
ary nuclei, where available. The Pa alpha emission is seen to be highly con
centrated on the nuclei, typically with very little emission extending beyo
nd a radius of 1 kpc. This survey was carried out primarily to search for s
ignatures of active nuclei via velocity-broadened hydrogen recombination or
the presence of the [Si VI] coronal line. These signatures are rare in the
present sample, occurring in only two of the 33 galaxies. The extinction t
o the hydrogen recombination lines is investigated via the Pa alpha /Br gam
ma line ratio. It is found that visual extinctions to the nuclei in excess
of 10 mag are relatively common among ULIRGs and that visual extinctions gr
eater than 25 mag are necessary to conceal a QSO emitting half the total bo
lometric luminosity. The ionized hydrogen regions in many ULIRGs are suffic
iently obscured that dust-enshrouded active galactic nuclei would remain hi
dden at 2 mum at the current level of sensitivity. The vibration-rotation l
ines of molecular hydrogen appear to be predominantly thermal in origin, wi
th effective temperatures generally around 2200 K. The relative nuclear vel
ocities between double nucleus ULIRGs are investigated, through which it is
inferred that the maximum deprojected velocity difference is similar to 20
0 km s(-1). This figure is lower than the velocities predicted by physical
models of strong interactions/mergers of large, gas-rich galaxies.