As extreme precipitation events become more frequent and intense, local-scale climate services are increasingly needed to help communities adapt. We here evaluate two fully-coupled convection-permitting Earth System Models for their ability to resolve mesoscale extreme weather events. Using the Integrated Forecasting System (IFS) and Icosahedral Nonhydrostatic Weather and Climate Model (ICON) within the Next Generation Earth Modelling Systems (nextGEMS) project, we evaluate their depiction of extreme precipitation with a focus on the Mediterranean region through a comparison with high resolution reanalysis, gridded observations, a regional climate model, and a large-ensemble lower-resolution climate model. The results are then compared at a coarser resolution globally with CESM2. For dry extremes, we find that the higher resolution and hybrid/explicit representation of convection of the nextGEMS models improve the representation of dry hour frequency and alleviates the drizzle bias observed in CMIP6 models. The explicit representation of convection in ICON helps create realistic dry spell lengths over land, but also generates overly intense convective precipitation. Generally, the nextGEMS models concentrate dry spells into limited frequency yet overly long periods. For wet extremes, the nextGEMS models properly high intensities of heavy precipitation, aside from overestimation in ICON over mountainous terrain. The models appear capable of resolving extreme weather systems like medicanes and tropical cyclones making them useful for extreme weather climatology studies. Overall, the depiction of wet and dry precipitation extremes in the Mediterranean region are representative of the nextGEMS’ models performance across the global mid-latitudes demonstrating the models’ value in simulating extreme weather systems.