Increasing interest in the airline engine industry has accelerated studies on the efficiency, performance, and reliability of aero engine materials. Development of materials meeting such requirements made a major contribution to the performance enhancement of engines. TiAl alloy has been accepted as a suitable candidate for structural materials at elevated temperatures because of its low density compared with the currently used Ni-based superalloys. In addition, the superior mechanical properties of TiAl alloy at high temperatures increase the potential uses of TiAl alloy as a practical material. However, due to insufficient oxidation resistance, its practical application is limited below 800℃, lower than that permissible by its mechanical properties. There have been two main approaches to enhancing oxidation resistance above 800℃ : alloy design and surface coating. Many reports indicate that the improvement of oxidation resistance favors surface coating rather than alloy design. To protect the substrate effectively in the air, not only the oxidation properties but also the resistance to thermal stress and chemical compatibility with the substrate should be taken into account when selecting the coating material. This accelerates studies on $L1_{2}$ -based alloys in the Al-Ti-Cr alloys system as coating materials for TiAl alloy. However, $L1_{2}$ -based alloys encountered a limitation for the application as a coating material because the mechanical properties, in particular cracking resistance, of $L1_{2}$ -based alloy could be degraded due to poor phase stability of $L1_{2}$ phase around 800℃. Henceforth, it is paramount to overcome the poor phase stability of $L1_{2}$ phase. In this study, the most appropriate coating composition among $L1_{2}$ -based alloys will be selected to overcome the insufficient phase stability and to maximize the mechanical properties, in particular cracking resistance. And the $L1_{2}$ -based alloy with most suitable composition will...