We conducted experiments for the solidiˆcation of a giant magnetostrictive TbFe2 alloys under a micro gravity condition using the JAMIC facility, Hokkaido, Japan. The kinetic process of the solidiˆcation of an intermetallic compound TbFe2 (C15 Laves phase) formed through a peritectic transformation was investigated. Attention was made with respect to dropping condition of a drop apparatus, and to melting and cooling manners of the alloy sample using a Cu-chill. The relation between the experimental conditions and microstructure of the samples was investigated. In the experiments from 1999 to 2001, we improved the dropping system to obtain a concrete picture of the kinetic process of solidification during under a microgravity. In addition, we measured temperature profiles of a sample during solidiˆcation process using thermocouples in order to search for an optimized experimental conditions such as drop timing and a manner of touching of the chill with a sample to cooling down in order to start of solidification accompanied by a peritectic transformation. In the microgravity condition, we were able to obtain microstructures containing high amounts of the TbFe2 phase compared with those obtained under the normal condition on the ground.