We have studied the dynamics and masses of a sample of ten nearby luminous and ultraluminous infrared galaxies (LIRGS and ULIRGs), using 2.3 micron CO absorption line spectroscopy and near-infrared H- and Ks-band imaging. By combining velocity dispersions derived from the spectroscopy, disk scale-lengths obtained from the imaging, and a set of likely model density profiles, we calculate dynamical masses for each LIRG. For the majority of the sample, it is difficult to reconcile our mass estimates with the large amounts of gas derived from millimeter observations and from a standard conversion between CO emission and H_2 mass. Our results imply that LIRGs do not have huge amounts of molecular gas (10^10-10^11 Msolar) at their centers, and support previous indications that the standard conversion of CO to H_2 probably overestimates the gas masses and cannot be used in these environments. This in turn suggests much more modest levels of extinction in the near-infrared for LIRGs than previously predicted (A_V~10-20 versus A_V~100-1000). The lower gas mass estimates indicated by our observations imply that the star formation efficiency in these systems is very high and is triggered by cloud-cloud collisions, shocks, and winds rather than by gravitational instabilities in circumnuclear gas disks.

14 pages, 2 figures, accepted to ApJ