We report the first in-situ powder X-ray diffraction (PXRD) study of the BaCO(3)-CeO(2)-In(2)O(3) and CeO(2)-In(2)O(3) systems in air over a wide range of temperature between 25 and 1200 degrees C. Herein, we are investigating the formation pathway and chemical stability of perovskite-type BaCe(1-x)In(x)O(3-delta) (x = 0.1, 0.2, and 0.3) and corresponding fluorite-type Ce(1-x)In(x)O(2-delta) phases. The potential direct solid state reaction between CeO(2) and In(2)O(3) for the formation of indium-doped fluorite-type phase is not observed even up to 1200 degrees C in air. The formation of the BaCe(1-x)In(x)O(3-delta) perovskite structures was investigated and rationalized using in-situ PXRD. Furthermore the decomposition of the indium-doped perovskites in CO(2) is followed using high temperature diffraction and provides insights into the reaction pathway as well as the thermal stability of the Ce(1-x)In(x)O(3-delta) system. In CO(2) flow, BaCe(1-x)In(x)O(3-delta) decomposes above T = 600 degrees C into BaCO(3) and Ce(1-x)In(x)O(2-delta). Furthermore, for the first time, the in-situ PXRD confirmed that Ce(1-x)In(x)O(2-delta) decomposes above 800 degrees C and supported the previously claimed metastability. The maximum In-doping level for CeO(2) has been determined using PXRD. The lattice constant of the fluorite-type structure Ce(1-x)In(x)O(2-delta) follows the Shannon ionic radii trend, and crystalline domain sizes were found to be dependent on indium concentration.