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This paper describes a technique to deliver video streams with constant perceptual quality of service (QoS) over time-varying packet erasure channels that support differentiated classes of service. During compression, the encoder estimates the distortion introduced at the decoder by each video packet both in case it is received and in case it is lost. Concealment and error propagation due to inter-frame prediction are taken into account. During transmission, an optimization algorithm assigns packets to different service classes according to the estimated distortion, the current channel status and a constraint on the desired quality at the receiver. This technique is compared with other video packet classification approaches in the specific case of a DiffServ IP network implementing the assured forwarding scheme. Network simulations show that the proposed technique delivers higher and more constant levels of perceptual QoS than traditional approaches. Moreover, the technique is characterized by reactiveness to congestion and fairness in the use of network resources.