The structure, magnetostriction and damping properties of Fe82Ga(18−x)Alx (x = 0, 5, 8, 12) alloys were analyzed. The anelastic response of Fe–18(Ga + Al) alloys was studied as a function of temperature (from 0 to 600 °C), frequency (from 0.01 to 200 Hz) and amplitude (from 0.0004% to 0.2%) of forced vibrations. The origin of the relatively high damping capacity of Fe–Ga–Al alloy at room temperature was determined by applying a magnetic field and different heat treatment regimes. The substitution of Ga by Al in Fe–18% Ga alloys was found to decrease magnetostriction and damping. The heat treatment of alloys influences the damping capacity of alloys more than variations of their chemical compositions. Thermally activated frequency and temperature-dependent anelastic effects in Fe–Ga–Al alloys were analyzed and the corresponding activation parameters for relaxation processes were evaluated. Internal friction effects caused by structural transformations were recorded and were found to be consistent with the A2 → D03 → L12 reaction. The physical mechanisms for all anelastic effects are discussed.