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As military, academic, and commercial computing systems evolve from autonomous entities that deliver computing products into network centric enterprise systems that deliver computing as a service, opportunities emerge to consolidate computing resources, software and information through cloud computing. Along with these opportunities come challenges, especially to service providers and operations centers that struggle to monitor and manage Quality of Service (QoS) for these services in order to meet customer service commitments. Traditional approaches fall short in addressing these challenges because they examine QoS from a limited perspective rather than from a System of Systems (SoS) perspective applicable to a net-centric enterprise system in which any user from any location can share computing resources at any time. This paper presents a SoS approach to provide QoS monitoring, management, and response for enterprise systems that delivers computing as a service through a cloud computing environment. Concrete examples are provided that identify the key components of this SoS and their application to real-world scenarios. Simulated results demonstrate the effectiveness of the approach for a representative scenario.