Summary: We study a generalization of the successive refinement coding problem called the sequential coding of correlated sources. In successive refinement source coding, one first describes the given source using a few bits of information and then subsequently improves the description of the same source when more information is supplied. Sequential coding differs from successive refinement in that the second-stage encoding involves describing a correlated source as opposed to improving the description of the same source. We introduce the notion of a coupled fidelity criterion to quantify perceived distortion in certain applications of sequential coding. We characterize the achievable rate region for this source coding problem and show that the rate region reduces to the successive refinement rate region when the two sources are the same. Then we consider the specific case of a pair of correlated Gaussian sources as an example. We give an explicit characterization that reveals an interesting generalization of a property of successive refinement of a single Gaussian source.