In this paper, we propose a new Scalable Video Coding (SVC) quality-adaptive peer-to-peer television (P2PTV) system executed at the peers and at the network. The quality adaptation mechanisms are developed as follows: on one hand, the Layer Level Initialization (LLI) is used for adapting the video quality with the static resources at the peers in order to avoid long startup times. On the other hand, the Layer Level Adjustment (LLA) is invoked periodically to adjust the SVC layer to the fluctuation of the network conditions with the aim of predicting the possible stalls before their occurrence. Our results demonstrate that our mechanisms allow quickly adapting the video quality to various system changes while providing best Quality of Experience (QoE) that matches current resources of the peer devices and instantaneous throughput available at the network state.