Neutron diffraction and mechanical spectroscopy techniques were applied to study phase transitions in Fe–Ga alloys with 25 and 27 at.% Ga. The following sequences of phase transitions at continuous heating and subsequent cooling in the 20–900 °C temperature range were recorded: D03 → L12 (limited amount) → A2(B2) was recorded at heating and A2(B2) → D03 at cooling for Fe-24.8Ga alloy, and the D03 → L12 → D019 → A2(B2) was recorded at heating and A2(B2) → L12 at cooling for Fe-27.4Ga alloy. Thus, the difference in 2.6 at.%Ga between two studied compositions with D03 structure leads to their different structures after heating to 900 °C. These transition sequences determine different temperature dependencies of elastic and anelastic properties. The D03 → A2(B2) transition (in Fe-25Ga) does not lead to a well-pronounced anelastic effect, in contrast the D03 → L12 transition (in Fe-27Ga) generates internal stresses due to a different rate of an increase in the lattice parameter with temperature and leads to a well-pronounced transient internal friction effect.