The encoding of a discrete memoryless multiple source <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\{( X_{i}, Y_{i})\}_{i=1}^{\infty}</tex> for reconstruction of a sequence <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\{Z_{i}\}_{i=1}^{\infty}}</tex> , with <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Z_{i} = F( X_{i}, Y_{i}); i = 1,2, \cdots</tex> is considered. We require that the encoding should be such that <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\{X_{i}\}_{i=1}^{\infty}</tex> is encoded first without any consideration of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\{Y_{i}\}_{i=1}^{\infty}</tex> , 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 <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H( X_{i}|Z_{i}, Y_{i}) = 0</tex> . Comparisons with the Slepian-Wolf problem and the Ahlswede-Korner-Wyner side information problem are carried out.