Studies of RE₅(Si_xGe_1-x)₄ alloys, where RE equals rare earth, have revealed a second-phase having a thin-plate morphology in essentially every alloy examined, independent of exact composition and matrix crystal structure. Identified as having a composition approximating Gd₅(Si_xGe_1-x)₃ and a hexagonal crystal structure in the Gd-based system, it has been suggested that the observed thin-plate second phases seen in this family of rare earth alloys are all most likely of the form RE₅(Si_xGe_1-x)₃. A number of interesting observations suggest that the formation of these second-phase plates is somewhat unusual. The purpose of this article is to investigate the stability of this second phase in Gd- and Er-based compounds. The stability was investigated as a function of thermal cycling and large-scale composition fluctuations. The results of scanning and transmission electron microscopy (SEM, TEM) studies indicate that the RE₅(Si_xGe_1-x)₃ phase is extremely stable once it forms in a RE₅(Si_xGe_1-x)₄ matrix.