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Based on a prototype presented in a prior publication, this research investigates the operational characteristics of a methane-fueled solid oxide fuel cell (SOFC) system with anode off-gas recirculation (AOGR) for electrical energy supply on sea-going vessels. The proposed first-principle system model utilizes a spatially segmented SOFC stack and lumped balance of plant components validated on the component level to accurately depict the steady-state and transient operating behavior. Five operational limitations are chosen to highlight permissible operating conditions with regard to stack and pre-reformer degradation. Steady-state operating maps are presented, emphasizing efficient operating conditions at maximum stack fuel utilization and minimal permissible oxygen-to-carbon ratio. Exemplary transient load changes illustrate increasing system control complexity caused by gas flow delays due to the spatially distributed plant layout. Actuation strategies are presented and underline the need for a top-level model predictive system controller to assure a dynamic and efficient operation within the defined constraints.