We design and analyze gossip algorithms for networks with correlated data. In these networks, either the data to be distributed, the data already available at the nodes, or both, are correlated. This model is applicable for a variety of modern networks, such as sensor, peer-to-peer and content distribution networks. Although coding schemes for correlated data have been studied extensively, the focus has been on characterizing the rate region in static memory-free networks. In a gossip-based scheme, however, nodes communicate among each other by continuously exchanging packets according to some underlying communication model. The main figure of merit in this setting is the stopping time -- the time required until nodes can successfully decode. While Gossip schemes are practical, distributed and scalable, they have only been studied for uncorrelated data. We wish to close this gap by providing techniques to analyze network coded gossip in (dynamic) networks with correlated data. We give a clean framework for oblivious network models that applies to a multitude of network and communication scenarios, specify a general setting for distributed correlated data, and give tight bounds on the stopping times of network coded protocols in this wide range of scenarios.