The anomalous amplitude‐dependent internal friction peak (P1) previously observed in cold‐worked and partially annealed dilute AlMg alloys around room temperature are systematically studied with polycrystalline Al–0.12 wt% Mg and single crystal Al–0.02 wt% Mg specimens with inverted torsion pendulums. This internal friction peak is found to be consisting of two separate peaks (P1′ and P1′). The amplitude peak associated with the lower temperature peak P1′ shifts toward lower amplitudes and that with P1′ shifts toward higher amplitudes with an increase of the temperature of measurement. The modulus curve corresponding to P1′ changes normally but that corresponding to P1′ changes abnormally. Conditions for the appearance of this double peak are described. The mechanism of these two peaks is suggested in terms of a dislocation kink model with consideration only of the short‐ranged interaction between the Mg solute atoms and the dislocations in aluminium.