Abstract In this work, exergy management strategies (ExMSs) for hybrid electric ground vehicles (HEVs) are developed. The main advantage of using the exergetic framework is the possibility of pursuing unconventional optimization goals that are inaccessible to the standard energy management strategy (EMS). For instance, in military applications, the critical goal of preventing thermal imaging detection from adversary units does not seem achievable with the conventional EMS. On the other hand, the exergy-based framework can be adopted to reduce the vehicle thermal emissions through the minimization of exergy terms related to heat exchange. Moreover, the overall efficiency of the vehicle can be increased through the minimization of the exergy destruction, a quantity that is not quantifiable by energy-based methods. In this paper, the exergetic model of a series hybrid electric military truck and the exergetic model of the electric induction generator are developed and used to formulate and solve two novel exergy management strategies aiming to minimize genset exergy destruction and thermal emissions, respectively. The optimal solutions to the EMS and ExMSs control problems are obtained through Dynamic Programming over two driving missions. The results show that ExMS for the minimization of exergy destruction achieves similar results to the standard EMS, while the ExMS for the minimization of thermal emissions obtains significantly lower thermal emissions compared to the EMS, effectively reducing the thermal imaging detection risk.