In recent years, peer-to-peer (P2P) and peer-assisted streaming have emerged as promising models for low-cost multimedia distribution to large scale user communities. In this paper, we study streaming of scalable video streams over these systems. Scalable video streams are composed of multiple layers and can easily be adapted according to the characteristics and needs of receivers. Thus, they can efficiently support a wide spectrum of heterogeneous peers participating in a P2P streaming system. We present an analytical model for forecasting the long-term behavior of a P2P streaming system with scalable video streams. Our analysis takes as inputs the characteristics of a dynamic P2P streaming system and the video streams. It then analytically computes the expected throughput of the streaming system and the expected video quality delivered to peers. The analysis also provides an upper bound on the maximum number of peers that can be admitted to the system at once (i.e., in flash crowd scenarios), while ensuring a certain video quality. We present a general analysis framework that can be customized to various practical P2P streaming systems with different characteristics. Then, we show the detailed analysis of a typical P2P streaming system and we explain how other systems can be analyzed using our model. We validate our analysis by comparing its results to those obtained from simulations, which confirm the accuracy of our analysis. Our analysis and simulations enable administrators of P2P streaming systems to predict the throughput and the video quality that can be delivered to users.