Copper(II) complexes of HPH-NH2 (L1) and HPHPY-NH2 (L2) peptides have been studied as small molecular models of lytic polysaccharide monooxygenases by pH-potentiometry and UV-vis, CD and EPR spectroscopy. The coordination properties of these ligands are fundamentally different from those of other non-protected N-terminal HXH-sequences concerning the metal binding ability of amide nitrogens. The proline units prevent the formation of fused chelates with the participation of amide nitrogens; therefore, instead of ATCUN-type {NH2,2N-,Nim} coordination, dimer complexes (Cu2HxL2, where x = -1, -2, and -3 for L1 and 1, 0, and -1 for L2) are formed in equimolar systems above pH 5. Using H2O2 as the oxidant and PNPG as the activated substrate, these dimer complexes were proved to be relevant functional models of LPMOs, even at neutral pH. Although the tyrosine residue in L2 participates in the coordination at pH 7-9.6, it does not seem to play a role in the oxidation process. In the presence of H2O2, the dimer complexes partially dissociate to form mononuclear hydroperoxo complexes, which are stable for 1-2 hours in equimolar concentrations of H2O2. On the other hand, with excess H2O2 both their formation and their decomposition are faster. The decay of (hydro)peroxo complexes, after longer reaction times, results in the evolution of dioxygen bubbles and the formation of Cu(I) (probably through catalytic disproportionation). However, in the presence of PNPG, the formation of dioxygen bubbles was not observed. Therefore, we assumed that the formed Cu(I) complexes bind H2O2 and enter into a similar catalytic cycle as suggested recently for native LPMOs.