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Understanding and exploring hydrological (H) or soil moisture (SM) drought due to meteorological (M) drought under changing climate is crucial for drought early warning. Previously, different methods were used to calculate drought propagation from one state (M to another [H or SM]). However, each method has its pros and cons and thus cannot describe appropriate propagation attributes. In this study, a time series analysis is carried out to explore the propagation process in the Yellow River Basin (YRB) and Hai River Basin (HRB) of China. Standardized Streamflow Index (SSI), Standardized SM Index (SSMI), and Standardized Precipitation Index (SPI) 1‐month time series were calculated using streamflow, satellite‐based SM, and precipitation from 1979 to 2016. The time series framework identifies the average drought propagation as 3.4–8.3 months (M–H) and 2.3–5 months (M–SM) in YRB, while 2.8–7.7 months (M–H) and 2.3–8.5 months (M–SM) in HRB. Cross‐wavelet analysis indicated that periodic characteristics of M drought are responsible for these droughts. Overall, the findings of this study may help to minimize the drought hazards posed by M droughts.