The Mediterranean (MED) Basin is a climate change hotspot that has seen drying and a pronounced increase in heatwaves over the last century. At the same time, it is experiencing increased heavy precipitation during wintertime cold spells. Understanding and quantifying the risks from compound events over the MED is paramount for present and future disaster risk reduction measures. Here, we apply a novel method to study compound events based on dynamical systems theory and analyse compound temperature and precipitation events over the MED from 1979 to 2018. The dynamical systems analysis quantifies the strength of the coupling between different atmospheric variables over the MED. Further, we consider compound warm-dry anomalies in summer and cold-wet anomalies in winter. Our results show that these warm-dry and cold-wet compound days are associated with large values of the temperature-precipitation coupling parameter of the dynamical systems analysis. This indicates that there is a strong interaction between temperature and precipitation during compound events. In winter, we find no significant trend in the coupling between temperature and precipitation. However in summer, we find a significant upward trend which is likely driven by a stronger coupling during warm and dry days. Thermodynamic processes associated with long-term MED warming can best explain the trend, which intensifies compound warm-dry events.