The temperature dependence of internal friction on frequency of ~3 Hz and ~60 Hz were studied in Invar Fe-35.0% Ni-0.49% Mn-0.03%C alloy after annealing at 1373 K and combined severe plastic deformation (SPD) by hydroextrusion and subsequent drawing with the total degree of accumulated deformation ε Σ = 4.69. The reduction of the relaxation IF peak intensity is observed in deformed sample of the alloy at ~380 K (the activation energy 0.82-0.93 eV) due to decreasing of mechanical and magnetomechanical relaxation losses the contribution of which is renewed after ageing of the deformed alloy. The damping growth nearby temperatures 780-820 K after combined SPD and partial its reduction after ageing of the alloy were revealed. The estimated activation energy of the relaxation process is 1.82-1.97 eV.