Intermetallic TiAl alloy are novel high-temperature materials which exhibit low densities and have excellent high-temperature creep strength. They are resistant against Ti-fire and therefore prime candidates for replacing the denser Ni-base alloys in the last turbine stages of jet-engines and in turbo-chargers of reciprocating engines. Wrought alloys, such as the TNM™ alloy investigated in this thesis, are expected to improve the strength and ductility of finished components as compared to cast parts. Cost efficient and reliable processing routes are key elements to the successful introduction of wrought TiAl into commercial applications. In the course of this thesis, diffraction methods were used to investigate this material class. Imaging methods and dilatometry as well as calorimetry were used to verify and complement the obtained data. Diffraction experiments were performed with two different sources of radiation. While X-ray diffraction gives high intensities for the main reflections of the occurring phases, ordering phenomena are difficult to detect. Neutron diffraction gives high intensities for the superstructure peaks of ordered phases while the intensities of the main peaks are very small. Consequently, in-situ neutron diffraction experiments were employed for determining the order to disorder transitions of the α₂ and β_o phase in the TiAl system. In-situ high energy X-ray diffraction experiments were performed at synchrotron sources and enabled investigating specimens in transmission mode. This is necessary to avoid results which are affected by the formation of a so-called α-case which is caused by the preferential evaporation of Al close to the surface at high temperatures. Furthermore the diffraction angles are low if high-energy X-rays are used which allows for bulky specimen environments such as furnaces and load-rigs. Microstructural processes occurring during hot compression were also investigated by means of a synchrotron diffraction method. To this end, a fast flat-panel detector operated at a frame rate of about 2 Hz was used. The course of phase fractions over temperature and the exact determination of the order to disorder transition temperatures contributed to the development of suitable processing routes for the investigated TiAl alloys. Furthermore, the influence of Mo additions on the phase diagram was revealed. A B19 type phase was found to act as a transitional phase that facilitates the precipitation of γ-phase from a supersaturated α₂ matrix in Ti-45 Al-3 Mo (in at%) alloy. Information on the microstructural processes occurring during hot-deformation is vital for optimization of the parameters for the thermo-mechanical processing of TiAl alloys and thereby contributes to the establishment of a stable and cost-efficient production route.