Peritectic couple growth (PCG) is an unusual growth form at which the peritectic and pro-peritectic solid phases solidify like a regular eutectic. To investigate the dynamics of PCG formation and growth, experiments with the transparent, organic peritectic alloy Tris(hydroxymethyl)aminomethane–Neopentylglycol are performed at the International Space Station. Fully planar and partly planar/cellular PCGs are found and analyzed. In any case, PCG starts with the formation of lateral bands from the peritectic phase that overgrow most of the pro-peritectic phase but not completely. During coupled growth, the remaining patches transform into rods and/or lamellae. Depending on the conditions, PCG either terminates by the disappearance of pro-peritectic rods or by transforming the rods into cells. The second mechanism goes hand in hand with the formation of a single-phase 2D layer at the top of a tilted interface. At low pulling velocities, planar pro-peritectic phase growth transforms into planar peritectic phase growth via PCG.