This paper aims to develop the first differentiated (earlywood—EW, latewood—LW, and total ring width—RW) dendrochronological series for ash (Fraxinus excelsior L.) and oak (Quercus robur L.) trees from the Republic of Moldova, and to analyze their climatic response and their spatio-temporal stability. For this, 18 ash and 26 oak trees were cored from the DobruÈ�a protected area, Republic of Moldova, Eastern Europe, and new EW, LW, and RW chronologies were developed for ash and oak covering the last century. The obtained results showed that the RW and LW have a similar climatic response for both species, while EW is capturing interannual climate variations and has a different reaction. The analyses performed with monthly climatic data revealed a significant and negative correlation with the mean air temperature and a significant and positive correlation with precipitation and the Standardized Precipitation-Evapotranspiration Index (SPEI) for both ash and oak. The temperature during the vegetation period has a strong influence on all tree-ring components of ash, while for oak the strong correlation was found only for LW. The positive and significant correlation between LW and RW with precipitation for both species, suggests that ash and oak are sensitive to the hydrological component and the precipitation is the main tree growth-limiting factor. Despite the significant correlation with precipitation and temperature for the whole analyzed period, the 25-year moving correlation analyses show that they are not stable in time and can switch from positive to negative or vice versa, while the correlation with SPEI3 drought index, which is a integration of both climatic parameters, is stable in time. By employing the stability map analysis, we show that oak and ash tree ring components, from the eastern part of the Republic of Moldova, have a stable and significant correlation with SPEI3 and scPDSI drought indices from February (January) until September, over the eastern part of Europe.