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The encoding of a discrete memoryless multiple source for reconstruction of a sequence , with is considered. We require that the encoding should be such that is encoded first without any consideration of , while in a second part of the encoding, this latter sequence is encoded based on knowledge of the outcome of the first encoding. The resulting scheme is called successive encoding. We find general outer and inner bounds for the corresponding set of achievable rates along with a complete single letter characterization for the special case . Comparisons with the Slepian-Wolf problem and the Ahlswede-Korner-Wyner side information problem are carried out.