Intermetallic titanium aluminides (TiAl) offer an enormous potential for high temperature applications due to their high specific strength, creep and oxidation resistance. However, their use for structural components is limited by their low ductility and fracture toughness. During service, along with a high number of load cycles, the material may also be subjected to unexpected impact loads, which requires therefore knowledge about dynamic material parameters for a damage-tolerant component design. Here we present a feasibility study to determine the fracture toughness of a third generation TiAl-alloy over a wide range of loading rates. Quasi-static crack resistance curves (R-curves) were determined using the direct current potential drop (DCPD) technique. The dynamic experiments were performed with a drop tower with impact velocities ranging from 1 to 10 m/s on pre-cracked SENB specimens. To exclude the influence of inertial forces, the measurements were carried out with strain gauges applied in the elastic near-field of the crack tip. Despite a critical consideration of possible systematic errors of this measurement method, it was found that the dynamic fracture initiation toughness slightly increases up to loading rates of K̇I = 106 MPa√m/s. The fracture behaviour of the material and possible reasons for the toughness increase are discussed based on comprehensive fractographic investigations as well as crack path analyses within the microstructure.