In-situ studies of the peritectic phase transition were performed under conditions close to chemical and thermal equilibrium in order to investigate the governing mechanism of both the peritectic reaction and the subsequent peritectic transformation using high-temperature laser-scanning microscopy in combination with the concentric solidification technique. Experiments have been conducted in the Fe–C and Fe–Ni systems in order to determine the role of solute diffusion on the observed reaction and transformation kinetics. The peritectic reaction as such as well as the subsequent peritectic transformation can be explained by diffusion-controlled mechanisms. Observations of the triple point L/γ/δ revealed that the peritectic reaction can be described as the solidification of γ along the L/δ interface, and new insights have been gained on the localized re-melting of δ during the peritectic reaction.