Knowing where and when rivers cease to flow provides an important basis for evaluating riverine biodiversity, biogeochemistry and ecosystem services. We present a novel modeling approach to estimate monthly time series of streamflow intermittence at high spatial resolution at the continental scale. Streamflow intermittence is quantified at more than 1.5 million river reaches in Europe as the number of no-flow days grouped into five classes (0, 1-5, 6-15, 16-29, 30-31 no-flow days) for each month from 1981 to 2019. Daily time series of observed streamflow at 3706 gauging stations were used to train and validate a two-step Random Forest modeling approach. Important predictors were derived from time series of monthly streamflow at 73 million 15 arc-sec (~500 m) grid cells that were computed by downscaling the 0.5 arc-deg (~55 km) output of the global hydrological model WaterGAP, which accounts for human water use. Of the observed perennial and intermittent station-months, 97.8% and 86.4%, respectively, are correctly predicted. Interannual variations of the number of intermittent months at intermittent reaches are satisfactorily simulated, with a median Pearson correlation of 0.5. While the spatial prevalence of intermittent reaches is underestimated, the number of intermittent months is overestimated in dry regions of Europe where artificial storage abounds. Our model estimates that 3.8% of all European reach-months and 17.2% of all reaches were intermittent during 1981-2019, predominantly with 30-31 no-flow days. Although estimation uncertainty is high, our study provides, for the first time, information on the continent-wide dynamics of intermittent rivers and streams.