The demand for materials that withstand harsh conditions in high-performance applications has increased drastically in recent years. Due to the predicted outstanding properties of high entropy alloys (HEAs) at elevated temperatures, this class of materials has attracted scientific attention. Within this thesis, the phase stability of TiAl-based HEAs, namely TiAlNbV-Mo and TiAlNbV-Mn systems, is investigated by first-principles calculations using Density Functional Theory (DFT) as implemented in the VASP code. The aim is to find elements for a HEA that promote the formation of a single-phase solid solution alloy and do not have the tendency to decompose into intermetallic phases. The information on the phase stability is provided by the evaluation of mixing energies. First of all, the stability of the HEAs and their possible decomposition products are evaluated at 0 K. Furthermore, the stabilizing effect of entropy is included by the contribution of the configurational entropy followed by the vibrational entropy estimated within the harmonic Debye model. Results obtained by the Exact Muffin-Tin Orbitals (EMTO) method are also presented for comparison. The predicted phase stabilities are discussed in the light of existing experimental literature results showing the evolution of microstructure before and after heat treatments. Overall, TiAlNbV-Mo has been identified as a kinetically stabilized HEA, whereas TiAlNbV-Mn decomposes into body-centred cubic and hexagonal Laves phases.