Intermetallic γ-TiAl based alloys have found applications in the low-pressure turbine of aircraft engines as well as in the turbocharger unit of automotive engines. However, these light-weight alloys must still be improved, through micro-alloying and tailoring the microstructure, to increase their creep resistance and consequently their maximum working temperature. In this work, a fully nano-lamellar advanced γ-TiAl based alloy doped with small amounts of C and Si is investigated in order to gain a deeper understanding of the atomic mobility mechanisms taking place at high temperature, thus controlling the creep properties. The study was approached through internal friction measurements up to 1223 K. We demonstrate that C has a notable influence on Ti diffusion in α ₂ phase, leading to an increase of the activation energy for Ti diffusion, which is assessed at ΔE _Ti(α ₂)=0.32 eV per at% C. An atomic model for the relaxation process is proposed capable to explain this phenomenon. An additional internal friction peak, which, up to now, remained hidden by the high temperature background, was observed in this nano-lamellar TiAl alloy and analyzed through a careful de-convolution of the internal friction spectra. This new relaxation process, with activation energy of 3.70 eV, is attributed to the short distance diffusion of Al atoms in the γ-TiAl lattice. A novel concept of stress-induced cell-lattice reorientation is proposed to explain this relaxation. Finally, a new experimental method to analyze the high temperature internal friction background, which is closely related to the creep behavior, was developed to study the fully nano-lamellar microstructure, whose high temperature background exhibits the highest activation energy ever measured in a γ-TiAl based alloy.