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Efficient peer-to-peer (P2P) video streaming is a challenging task due to time-varying nature of both the number of available peers and network/channel conditions. This paper proposes a novel adaptive P2P video streaming system, which features: (i) a new flexible multiple-description coding (F-MDC) framework, such that the number of base and enhancement descriptions, and the rate and redundancy level of each description can be adapted on the fly (by only post-processing of the encoded bitstream), and (ii) a new adaptive TCP-friendly rate-controlled (TFRC), on-demand, many-to-one P2P video streaming solution based on the proposed F-MDC framework. We extend the highly scalable video coder , to MDC within the proposed F-MDC framework. Optimization of the design parameters of the proposed F-MDC method is discussed within the context of the proposed adaptive P2P streaming solution, where the number and quality of available streaming peers/paths are a priori unknown and vary in time. Experimental results, by means of NS-2 network simulation of a P2P video streaming system, show that adaptation of the number, type of descriptions and the rate and redundancy level of each description according to network conditions yields significantly superior performance when compared to other scalable MDC schemes using a fixed number of descriptions/layers with fixed rate and redundancy level.