How to explore an inherent linkage between non-equilibrium liqulid/solid transformation (LST) and subsequent solid-state transition (SST) is becoming more and more important for material preparation Applying highly undercooled solidification and melting spinning single-phase supersaturated solid solution (SSSS) was prepared for immiscible Fe-Cu and low-solid-solubility Fe-B alloys respectively By performing isothermal annealings at temperatures for the above SSSS an Inherent linkage between non-equilibrium LST and solid-state grain growth has been studied in terms of an extended dendrite growth model and solute trapping model (for non-equilibrium solidification) and a numerical and an analytical thermo-kinetic model (for solid-state grain growth) For Fe-Cu SSSS a relation between the metastable equilibrium grain size and the initial melt undercooling was derived whereas for Fe-B SSSS a relation between the metastable equilibrium grain size and the ribbon thickness/rotational speed (In melt spinning) was deduced The model prediction is consistent with the experimental result indicating that the solid-state grain growth stops as a result of decrease in GB energy due to solute segregation to GBs This further certifies that for the alloys considered the final microstructure is determined by both the non-equilibrium LST and the solid-state grain growth including GB segregation (C) 2010 Elsevier B V All rights reserved