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The rapid growth of new information services and business-oriented applications entails the consideration of quality of service (QoS) in content distribution. This paper investigates the QoS-aware replica placement problems for responsiveness QoS requirements. We consider two classes of service models: replica-aware services and replica-blind services. In replica-aware services, the servers are aware of the locations of replicas and can therefore optimize request routing to improve responsiveness. We show that the QoS-aware placement problem for replica-aware services is NP-complete. Several heuristic algorithms for fast computation of good solutions are proposed and experimentally evaluated. In replica-blind services, the servers are not aware of the locations of replicas or even their existence. As a result, each replica only serves the requests flowing through it under some given routing strategy. We show that there exist polynomial optimal solutions to the QoS-aware placement problem for replica-blind services. Efficient algorithms are proposed to compute the optimal locations of replicas under different cost models.