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Oxygen and carbon are important elements in stellar populations. Their behavior refers to the formation history of the stellar populations. C and O abundances would also obviously influence stellar opacities and the overall metal abundance Z. With observed high-quality spectroscopic properties, we construct stellar models with C and O elements to give more accurate ages for 70 metal-poor dwarfs, which have been determined to be high-α halo, low-α halo, and thick-disk stars. Our results show that high-α halo stars are somewhat older than low-α halo stars by around 2.0 Gyr. The thick-disk population has an age range in between the two halo populations. The age distribution profiles indicate that high-α halo and low-α halo stars match the in situ accretion simulation by Zolotov et al., and the thick-disk stars might be formed in a relatively quiescent and long-lasting process. We also note that stellar ages are very sensitive to O abundance, since the ages clearly increase with increasing [O/Fe] values. Additionally, we obtain several stars with peculiar ages, including 2 young thick-disk stars and 12 stars older than the universe age. [ABSTRACT FROM AUTHOR]