In-situ Laser Scanning Confocal Microscopy observations are presented that assess the influence of undercooling before the initiation of the peritectic transition in a Fe-4.2wt%Ni alloy on the resulting kinetics of the peritectic reaction and transformation. In a series of experiments varying the cooling rate, increasing the cooling rate led to a lower temperature at the L/ interface. The resulting peritectic reaction changed from slow 840m/s - 1500m/s, with limited growth into the to rapid ~11mm/s with significant growth into . In continuous cooling experiments when the nucleation temperature was low, growth into was high and the reacting species was observed to propagate along the liquid/delta-ferrite interface at a rate of ~11mm/s. The peritectic reaction rate did not appear to be a function of temperature over a measured nucleation temperature range of 5 K. Conversely, the growth rate of austenite into the delta-ferrite in the first 0.03 seconds was observed to increase from 1.5mm/s to 8mm/s as the measured temperature at nucleation decreased.