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Determining the absolute dates of specimens by means of thermoluminescent analysis is an important method to the dating of cultural relics unearthed from archaeological explorations. Using the fine-grain thermoluminescent method, the authors analyzed ancient ceramics unearthed from two sites of capital construction in Changsha City. They obtained 15 dates, of which the relative errors account for 8% and two data are unacceptable. Research on the factors of the errors indicates that the application of thermoluminescent analysis in the dating of specimens requires some preconditions and that the fine-grain method, therefore, has its limitations.