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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-$\alpha$ halo, low-$\alpha$ halo and thick-disk stars. Our results show that high-$\alpha$ halo stars are relatively older than low-$\alpha$ halo stars by around 2.0 Gyr. The thick-disk population has an age range between the two halo populations. The age distribution profiles indicate that high-$\alpha$ halo and low-$\alpha$ 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., Comment: 23 pages, 5 figures, ApJ accepted