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Underwater Acoustic Sensor Networks (UW-ASNs) consist of stationary or mobile nodes such as Autonomous Underwater Vehicles (AUVs), which may be classified as propeller-driven vehicles and gliders, that are equipped with a variety of sensors for performing collaborative monitoring tasks. The missions entrusted to the AUVs in this work are critical to human life and property, are bound by severe time and energy constraints, and involve a high degree of inter-vehicular communication. In this work, a task allocation framework for networked AUVs that participate as a team to accomplish critical missions is developed. The team formed as a result of this task allocation framework is the subset of all deployed AUVs that is best suited to accomplish the mission while adhering to the mission constraints. Research specific to this area has been limited, hence a task allocation framework for networked AUVs to accomplish critical missions is proposed.