In this work we analyze at a structural level the mechanism by which Cu(II) and Zn(II) ions compete for binding to the Aβ peptides that is involved in the etiology of Alzheimer's disease. We collected X-ray absorption spectroscopy data on samples containing Aβ with Cu and Zn at different concentration ratios. We show that the order in which metals are added to the peptide solution matters and that, when Zn is added first, it prevents Cu from binding. On the contrary, when Cu is added first, it does not (completely) prevent Zn binding to Aβ peptides. Our analysis suggests that Cu and Zn ions are coordinated to different numbers of histidine residues depending on the [ion]:[peptide] concentration ratio.