Analysis of ship propulsion system performance is often performed using detailed hydrodynamic models to assess load changes, which are subsequently compared to static engine limits, or by detailed engine models that are rarely integrated with sufficiently detailed propulsion models for load change estimation. To investigate the dynamic engine (overloading) behaviour and ship propulsion performance under various heavy operating conditions, a Mean Value First Principle Parametric (MVFPP) engine model is integrated into a ship propulsion system model in this paper. An upgraded thermodynamic-based MVFPP model for two-stroke marine diesel engines is presented, in particular a newly developed MVFPP gas exchange model. Based on the integrated propulsion system model of a benchmark ocean-going chemical tanker, the engine dynamic behaviour during ship acceleration, deceleration and crash stop has been investigated. Results show that, during dynamic processes, the engine could be thermally overloaded even if the engine power trajectory is inside the static engine operating envelope. The paper contributes to finding proper indicators for thermal overloading of modern two-stroke marine diesel engines. It is demonstrated that when matching the engine with the propeller and designing the ship propulsion control system, not only the static engine operating envelope, but also the dynamic engine behaviour should be considered. • Mean Value First Principle Parametric (MVFPP) model for 2-stroke marine diesel engine. • Novel approach to two-zone modelling of scavenging process. • MVFPP model is balanced choice to predict engine behavior in drive system simulation. • Static performance maps & limits inadequate for prediction of engine dynamic behavior. • MVFPP model can provide deeper understanding of thermal overloading of engines.