This work is focused on the coupling of two complex models based on different underlying physics: a vapor compression refrigerating system and its electrical drive system. The main challenge was to correctly handle the large simulation time constant difference which is three orders of magnitude smaller for the electrical system. The two models have been originally developed following very specific requirements (i.e. high numerical robustness and low time consumption) for their suitable use in simulations of large and complex aircraft Environmental Control Systems (ECS). The direct coupling of both systems has been observed to cause numerical instabilities, therefore,a coupling approach based on non-invasive dynamic relaxations has been implemented. The resulting combined simulations have shown to be numerically stable for the complete range of operating conditions and for a wide range of time steps.