Abstract: Meteorological drought is an important driving factor of agriculture drought in their inherent correlation. Characteristics and estimation of agricultural drought response to meteorological drought can contribute to understanding the mechanism of drought evolution, and assessment of drought mitigation measures. However, most previous studies are lacking in the spatiotemporal continuity of drought evolution. In this study, the spatiotemporal dynamic evolution of droughts in the Heihe River Basin during 1961-2014 was analyzed using a three-dimensional identification method, where the standardized precipitation evapotranspiration index (SPEI) and agriculture standardized precipitation index (aSPI) were used to evaluate the meteorological drought and agricultural drought. A spatiotemporal matching criterion of drought event was proposed to determine the event pair of meteorological-agricultural drought, and thereby a response model of drought variables was established based on the spatiotemporal characteristics of agriculture drought response to meteorological drought. The results showed that 1) three-dimensional perspective can benefit to recognition for the dynamic evolution rules of drought events. Six drought variables were selected as indicators, including drought duration, area, severity, intensity, center and migration trajectory, to analyze the drought evolution for Heihe River basin in 1961-2014. Specifically, the most severe meteorological drought event (No.25) originated in Linze county in June 1970, showing the drought-affected area of only 843.14 km2. The drought spread rapidly to the whole study area in July, with the drought-affected area of 42 400 km2, accounting for about 87% of the study area, and the drought center is located in the middle of Sunan county. The subsequent drought moved approximately 13.86 km in the northwest direction from August to September 1970 with the decrease of drought intensity and affected area. In the next two months, the drought areas continuously decreased, and mainly concentrated in Gaotai, Linze and Qilian county. The second peak of this drought occurred from December 1970 to March 1971, the drought-affected areas accounting for 54%-71% of the study area, with the drought severity of 43 700 km2•month. The drought center moved 94.96 km toward southeast to eastern Qilian county, and finally diminished there from April to July 1971. The continuous droughts in autumn, winter and spring generally originated from the middle-stream, and gradually migrated to the upstream along the southeast direction, particularly that the rate of drought migration was relatively high in the upstream. 2) The matching results of drought events based on spatiotemporal scale can ensure that the complex relationship between meteorological and agricultural drought well agrees with the practical situation, with the high accuracy of response analysis. The drought events after successful matching demonstrate the specific characteristics, including prolonged duration, enhanced intensity and increase affected area. 3) The optimal response models of drought duration, area and severity between meteorological and agricultural drought follow the quadratic polynomial, the exponential function and exponential function, respectively. This finding can provide an insightful understanding to accurate evaluate the spatiotemporal dynamic evolution and the response relationship of droughts.