By exploiting the far-infrared(FIR) and radio correlation, we have performed the Likelihood-Ratio analysis to identify optical counterparts to the far-infrared sources in the Lockman Hole. Using the likelihood ratio analysis and the associated reliability, 44 FIR sources have been identified with radio sources. Redshifts have been obtained for 29 out of 44 identified sources. One hyper-luminous infrared galaxy (HyLIRG) with and four ultraluminous infrared galaxies (ULIRGs) are identified in our sample. The space density of the FIR sources at z = 0.3-0.6 is 4.6times 10^{-5}Mpc^{-3}, implying a rapid evolution of the ULIRG population. Most of ISO FIR sources have their FIR-radio ratios similar to star-forming galaxies ARP 220 and M82. At least seven of our FIR sources show evidence for the presence of an active galactic nucleus (AGN) in optical emission lines, radio continuum excess, or X-ray activity. Three out of five (60%) of the ULIRG/HyLIRGs are AGN galaxies. Five of the seven AGN galaxies are within the ROSAT X-ray survey field, and two are within the XMM-Newton survey fields. X-ray emission has been detected in only one source, 1EX030, which is optically classified as a quasar. The non-detection in the XMM-Newton 2-10 keV band suggests a very thick absorption obscuring the central source of the two AGN galaxies. Several sources have an extreme FIR luminosity relative to the optical R-band, L(90mumathrm{m})/L(R) > 500, which is rare even among the local ULIRG population. While source confusion or blending might offer an explanation in some cases, they may represent a new population of galaxies with an extreme activity of star formation in an undeveloped stellar system -- i.e., formation of bulges or young ellipticals.
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