Copper binding to α-synuclein (aS) and to amyloid-β (Ab) has been connected to Parkinson's and Alzheimer's disease (AD), respectively, because Cu ions can modulate the peptide aggregation, and these Cu ⋅ peptide complexes can catalyse the production of reactive oxygen species (ROS). In a significant proportion of AD brains, aggregation of aS and Ab has been detected, and it was proposed that Ab and aS interact with each other. Thus, we investigated the potential interactions of Ab and aS through their binding of copper(I) and copper(II). Additionally, β-synuclein (bS) was investigated, due to its additional methionine residue, a potential Cu(I) ligand. We found that: 1) the peptides containing the Cu-binding domains Ab1-16, aS1-15 and bS1-15 have similar affinities towards Cu(II) and towards Cu(I), with Ab1-16 being slightly stronger, 2) in the case of Cu(I), the additional Met residue in bS1-15 increased the affinity slightly, 3) the exchange of Cu(I/II) between the two peptides is rapid (≤ ms), 4) a/bS1-15 and Ab1-16 form a heterodimeric complex with Cu(II), 5) Cu(I) probably promotes a transient ternary complex, 6) the different Cu(I/II) coordination of Ab1-16, aS1-15 and bS1-15 impacts the capacity to produce ROS and to oxidise catechol, and 7) when Ab1-16, aS1-15 and Cu are present, the ROS production more closely resembles that by Ab1-16. The work gives insights into the coordination chemistry of these related peptides, and the relevance of coordination differences, the ternary complex and ROS production are discussed.