We investigate the nature of far-infrared (70 um) and hard X-ray (3-24 keV) selected galaxies in the COSMOS field detected with both Spitzer and Nuclear Spectroscopic Telescope Array (NuSTAR). By matching the Spitzer-COSMOS catalog against the NuSTAR-COSMOS catalog, we obtain a sample consisting of a hyperluminous infrared galaxy with log(L_IR/L_sun) > 13, 12 ultraluminous infrared galaxies with 12 < log(L_IR/L_sun) < 13, and 10 luminous infrared galaxies with 11 < log(L_IR/L_sun) < 12, i.e., 23 Hy/U/LIRGs in total. Using their X-ray hardness ratios, we find that 12 sources are obscured active galactic nuclei (AGNs) with absorption column densities of N_H > 10^22 cm^-2, including several Compton-thick (N_H ~ 10^24 cm^-2) AGN candidates. On the basis of the infrared (60 um) and intrinsic X-ray luminosities, we examine the relation between star-formation (SF) and AGN luminosities of the 23 Hy/U/LIRGs. We find that the correlation is similar to that of optically-selected AGNs reported by Netzer (2009), whereas local, far-infrared selected U/LIRGs show higher SF-to-AGN luminosity ratios than the average of our sample. This result suggests that our Hy/U/LIRGs detected both with Spitzer and NuSTAR are likely situated in a transition epoch between AGN-rising and cold-gas diminishing phases in SF-AGN evolutional sequences. The nature of a Compton-thick AGN candidate newly detected above 8 keV with NuSTAR (ID 245 in Civano et al. 2015) is briefly discussed.
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