A reduction of the weight of the rotating components in a jet engine allows to lower fuel consumption and increase the efficiency. This is achieved primarily by replacing conventional nickel-based alloys in the low-pressure turbine (LPT) with titanium aluminides (TiAl). Besides their high specific strength, they also exhibit good creep properties and oxidation resistance. Since TiAl has limited ductility and fracture toughness compared to conventional nickel-based alloys, it is important to understand the microstructural influences on these parameters. During this master’s thesis, threshold and fracture toughness measurements were performed on two different alloys (BMBF3 and TNMZ4010) with different heat treatment conditions. Since the used samples were additively manufactured by Selective Electron Beam Melting (SEBM), two orientations per sample were tested to study the directional dependence of the properties. Subsequently, the fracture surfaces were investigated using a scanning electron microscope (SEM) to reveal microstructure-property relationships. In addition to the measured threshold and fracture toughness values, crack resistance curves (R-curves) and fatigue crack growth curves (FCG-curves) were also determined. Furthermore, driving force diagrams were constructed, do be able to make statements about the maximum tolerable load or load amplitude. All obtained results are compared with the properties of a selected heat treatment condition of an established TNM alloy. The investigations showed that large α2/γ-colonies lead to a high fracture toughness but have almost no positive effect on the long crack threshold. On the other hand, duplex microstructures with small α2/γ-colonies and thick lamellae show high long crack threshold values and low fracture toughness values. Specimens with high fractions of globular γ-phase show both, low fracture toughness values and low long crack threshold values. Some investigated microstructures reveal a strong directional dependence of the fracture mechanical properties. Thus, the variations of the microstructures have a significant effect on the properties and it is still necessary to investigate, which of the new possible microstructure combinations are able to reach the level of the established TNM alloy.