Tau protein is present in significant amounts in neurons, where it contributes to the stabilization of microtubules. Insoluble neurofibrillary tangles of tau are associated with several neurological disorders known as tauopathies, among which is Alzheimer's disease. In neurons, tau binds tubulin through its microtubule binding domain which comprises four imperfect repeats (R-1-R-4). The histidine residues contained in these fragments are potential binding sites for metal ions and are located close to the regions that drive the formation of amyloid aggregates of tau. In this study, we present a detailed characterization through potentiometric and spectroscopic methods of the binding of copper in both oxidation states to R-1 and R-3 peptides, which contain one and two histidine residues, respectively. We also evaluate how the redox cycling of copper bound to tau peptides can mediate oxidation that can potentially target exogenous substrates such as neuronal catecholamines. The resulting quinone oxidation products undergo oligomerization and can competitively give post-translational peptide modifications yielding catechol adducts at amino acid residues. The presence of His-His tandem in the R-3 peptide strongly influences both the binding of copper and the reactivity of the resulting copper complex. In particular, the presence of the two adjacent histidines makes the copper(I) binding to R-3 much stronger than in R-1. The copper=R-3 complex is also much more active than the copper-R-1 complex in promoting oxidative reactions, indicating that the two neighboring histidines activate copper as a catalyst in molecular oxygen activation reactions.