Detecting droughts as early as possible is important in avoiding negative impacts on economy, society, and environment. To improve drought monitoring, we studied drought propagation (i.e., the temporal manifestation of a precipitation deficit on soil moisture and streamflow). We used the Standardized Precipitation Evapotranspiration Index (SPEI), Standardized Streamflow Index (SSI), and Standardized Soil Moisture Index (SSMI) in three drought-prone regions: Sonora (Mexico), Maipo (Chile), and Mendoza-Tunuyán (Argentina) to study their temporal interdependence. For this evaluation we use precipitation, temperature, and streamflow data from gauges that are managed by governmental institutions, and satellite-based soil moisture from the ESA CCI SM v03.3 combined data set. Results confirm that effective drought monitoring should be carried out (1) at river-basin scale, (2) including several variables, and (3) considering hydro-meteorological processes from outside its boundaries.