Abstract: A theoretical study is developed on the evolution and mechanism of an ordering coupled phase separation, and on the origin of a resultant tweed microstructure. It is found that long-range elastic interaction among atoms with different atomic sizes plays a key role in the phase sep aration, and that the evolution of the phase separation is very similar to that Of conventional spinodal decomposition except that the separation is dependent on an elastic interaction order ing (EIO). This "EIO coupled spinodal decomposition" is shown to exhibit a periodical or tweed microstructure being accompanied by an EIO. It is also found that a large atomic size factor yields a large positive contribution of EIO to spinodal decomposition. Generally it is thermodynamically and kinetically favorable for the EIO to precede the onset of spinodal decomposition,though the former is not separable from the latter as a whole. We suggest that an initially disordered solid solution undergoes an EIO first, and then the partially ordered solid solution starts to decompose via a spinodal mechanism. Solute-enriched regions increase their degree of order along with an increase in solute content, and solute-depleted regions decrease their degree of order together with a decrease of solute content. The final microstructure is characterized by a periodical array of highly ordered solute-enriched regions and nearly disordered solute-depleted regions. The notion of EIO coupled spinodal decomposition is in general agreement with the transformation behaviour of a large number of alloy systems.