We have studied a binary Au-Cu single crystal by mechanical spectroscopy. Upon very slow cooling from high temperatures, additional relaxation peaks arise at lower frequencies in isothermal spectra after the disappearing of the Zener peak below 665 K due to ordering. A high transient peak is visible at 660 K and it progressively disappears on cooling until 625 K. Another high peak is clearly visible upon following heating until 660 K. Above that temperature it decreases in parallel with the increase of the Zener peak. If the ordered structure is obtained by slowly heating the sample that has been quenched from the disordered state, no low-frequency peak is visible in the isothermal spectra, only a much lower background, which further decreases in parallel with the reappearance of the Zener peak. The low frequency relaxations are possibly due to the movement of antiphase boundaries and twin interfaces in the ordered structures.