We present first results from our Very Large Telescope large program to study the dynamical evolution of ultraluminous infrared galaxies (ULIRGs), which are the products of mergers of gas-rich galaxies. The full data set consists of high-resolution long-slit H- and K-band spectra of 38 ULIRGs and 12 QSOs (in the range 0.042 < z < 0.268). In this paper, we present the sources that have not fully coalesced and therefore have two distinct nuclei. This subsample consists of 21 ULIRGs, the nuclear separation of which varies between 1.6 and 23.3 kpc. From the CO band heads that appear in our spectra, we extract the stellar velocity dispersion, σ, and the rotational velocity, V_rot. The stellar dispersion equals 142 km s^-1 on average, while V_rot is often of the same order. We combine our spectroscopic results with high-resolution infrared (IR) imaging data to study the conditions for ULIRG activity in interacting pairs. We find that the majority of ULIRGs are triggered by almost equal-mass major mergers of 1.5 : 1 average ratio. Less frequently, 3 : 1 encounters are also observed in our sample. However, less violent mergers of mass ratio >3 : 1 typically do not force enough gas into the center to generate ULIRG luminosities.