Ultraluminous infrared galaxies (ULIRGs) with multiple (>= 3) nuclei are frequently observed. It has been suggested that these nuclei are produced by multiple major mergers of galaxies. The expected rate of such mergers is, however, too low to reproduce the observed number of ULIRGs with multiple nuclei. We have performed high-resolution simulations of the merging of two gas-rich disk galaxies. We found that extremely massive and compact star clusters form from the strongly disturbed gas disks after the first or second encounter between the galaxies. The mass of such clusters reaches similar to 10(8) M-circle dot and their half-mass radii are 20-30 pc. Since these clusters consist of young stars, they appear as several bright cores in the galactic central region (similar to kpc). The peak luminosity of these clusters reaches similar to 10% of the total luminosity of the merging galaxy. These massive and compact clusters are consistent with the characteristics of the observed multiple nuclei in ULIRGs. Multiple mergers are not necessary to explain multiple nuclei in ULIRGs.