Based on our earlier work on thermal stabilization of Sn-Ni peritectic alloy where both the primary and peritectic phases are intermetallic compound phases in an imposed temperature gradient, the migration of the solid/liquid interface and its position during thermal stabilization have been analyzed. The thermal stabilization after which the directional solidification takes place determines the initial growth condition of directional solidification, like the position (migration) of the solid/liquid interface. The migration of the solid/liquid interface is a rather interesting and complex phenomenon, which is directly determined by the relationship between three different melt concentrations: melt concentration of the boundary layer adjoining the solid/liquid interface C-L, melt concentration of the complete-mixed zone C-m and the equilibrium melt concentration at the solid/liquid interface C-e. Both the downward migration by remelting of solid phases and upward migration by resolidification of solid phases have been discussed in this work. Downward/upward migration of the solid/liquid interface continues if C-L is larger/smaller than C-e. During migration of the solid/liquid interface, the solute boundary layer is gradually destroyed. Analytical models have been established to describe the migration of the solid/liquid interface which is rather complex in peritectic systems.