Understanding phenomena that occur during gradient annealing and initial transient of Bridgman-type directional solidification processes is essential for producing high-performance materials with specific properties. An experiment with alternating long time gradient annealing and directional solidification periods was performed on the International Space Station, using a near-peritectic transparent TRIS-NPG alloy. It transpired that accumulation of solute ahead of the solid/liquid interface continued to progress and that steady-state growth conditions were never achieved. The results demonstrate that (i) liquid being squeezed out from the mush during the long time gradient annealing period disables the formation of a flat interface; (ii) a thermal bias caused a slightly tilted planar solidification front; and (iii) growth of the metastable pro-peritectic α-phase led to the formation of a supersaturated solid that solidified with an intriguing low growth rate.