Anelasticity of Fe-(16−21)at% Ga-RE (rare earth RE = La, Tb, Dy, Er, Yb elements) alloys at room and elevated temperatures is studied in a sub-resonance mechanical spectroscopy. Two thermally-activated and two transient effects are recorded in most of the studied alloys. To explain these phenomena, structure and phase transitions in several binary and ternary Fe-Ga alloys are investigated. The D03 ordering of rapidly cooled alloys with the A2 structure at heating at around 300 °C and the disordering at heating and the D03 ordering at cooling around 500 °C for annealed samples are proved using three in situ techniques: neutron diffraction, vibrating sample magnetometry, and internal friction and supported by positron annihilation experiments. Thermally activated transitory effects are tentatively explained by stress-induced reorienta-tion of Ga-Ga, vacancy-vacancy pairs, and carbon atoms jumps.