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In this paper, we propose a method for peer assisted on demand delivery of scalable video using an optimal, distributed caching algorithm for cache constrained peers. We assume that there are one or more content delivery servers that are provisioned to support delivery of the base layer for all of the peers, and the enhancement layer is only supported for a fraction of peers. It has been shown that in such an application, peer assisted content distribution improves the delivery of the content. In this paper, we use peer assisted delivery of the enhancement layer and show that in a cache constrained video-on-demand environment, availability of the cached content becomes a bottleneck. By using peer arrival rates and supply-demand analysis of the peers, we propose better caching policies at each peer. One proposed policy (referred to as "static optimal") optimizes the utility of the currently available caching opportunities. The other proposed policy (referred to as "dynamic programming" solution) on the other hand performs utility optimization by further considering the future caching opportunities during the streaming operation. Experimental results show that the proposed methods allow more peers to access the enhancement layer; hence, more peers experience improved video quality compared to traditional caching methods.