We report the results of searches for solar axions and galactic dark matter axions or axion-like particles with CDEX-1 experiment at the China Jinping Underground Laboratory, using 335.6 kg-days of data from a p-type point-contact germanium detector. The data are compatible with the background model and no excess signals are observed. Limits of solar axions on the model independent coupling from Compton, bremsstrahlung, atomic-recombination and deexcitation channel and $g^{}{AN}\times g{Ae}<6.1\times10^{-17}^{57}$Fe M1 transition at 90 % confidence level are derived. Within the framework of the DFSZ and KSVZ models, our results exclude the axion mass heavier than 0.9 eV/c and 173 eV/c, respectively. The derived constraints for dark matter axions below 1 keV improves over the previous results.

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