Extreme weather, such as heavy precipitation and strong winds, can co‐occur, resulting in larger socio‐economic impacts than the linear sum of their components. These are termed 'compound extremes' and are challenging to forecast even a few days before.With this aim, we investigate the 'wet' and 'windy' extremes associated with Eastern Mediterranean cyclones in winter. We combine insights from a synoptic classification algorithm, traditional atmospheric analysis techniques, and dynamical systems theory. In phase space, the latter quantifies atmospheric states' co‐recurrence ratio (α) and persistence (Θ‐1). We base the analysis on ERA5 at various pressure levels and time lags.Our analysis is two‐fold; First, we define compound dynamical extremes (CDE) based on upper and lower deciles of α and Θ‐1, linking them to the synoptic patterns. We find that CDEs are related to the depth and location of the surface cyclone and upper‐level trough. Then, we show that high co‐recurrence and persistence are associated with heavier precipitation and stronger wind speed. Second, we define compound extremes (CE), the upper 5% of precipitation intensity and wind velocity co‐occurring simultaneously. We link these back to the dynamical system metrics anomalies. Finally, we compare CEs with individual extremes and cyclone climatology. We find that CEs display significantly higher co‐recurrence and persistence than individual extremes. Indeed, days with high co‐recurrence and persistence anomalies are ~ 2‐18 times more likely to be allied with extreme weather, depending on the extreme type, than low co‐recurrence and persistence. Moreover, we show that the upper levels are significantly more persistent than the surface flow during a CE. The mid‐February 2012 'wet' and 'windy' CE case study strengthened the abovementioned climatological findings.To conclude, the dynamical systems viewpoint is a valuable complement to understanding the dynamics of CEs in the Eastern Mediterranean. We foresee it to be fruitfully applied to other CEs and regions.This article is protected by copyright. All rights reserved.