Cu-modified zeolites have enormous potential as the catalysts facilitating the conversion of methane to methanol. It becomes important to investigate the active sites and the reaction mechanisms involved. In this paper, several spectroscopic methods such as UV-vis diffuse reflectance spectroscopy (UV-vis DRS), pulse electron paramagnetic resonance (EPR), diffuse reflectance Fourier transform infrared spectroscopy, and solid-state (C-13 MAS) NMR have been employed to characterize the state of the Cu sites and the intermediates formed during the catalyst activation and methane-tomethanol transformation on Cu/H-ZSM-5 zeolite with low (0.10 wt %) Cu content. UV-vis DRS and EPR data imply the presence of two types of Cu2+ cations bound to the zeolite framework Si-O--Al sites (Z). One of them is a species of the type Z[Cu(II)O] or Z[Cu(II)(OH)] with extra-framework O- or OH- ligands. The other one refers to Z(2)Cu(II) species without extra-framework O-containing ligands. CW EPR studies reveal that the Z(2)Cu(II) species are the major part of the Cu(II) sites present in the zeolite. H-1 HYSCORE and DRIFTS data are supportive of the formation of a molecular complex of methane and Z(2)Cu(II) species, with a strongly polarized C-H bond and a 3.3 angstrom separation between the hydrogen atom of methane and Cu. C-1(3) MAS NMR provides evidence for the formation of both the surface methoxy intermediate and physisorbed methanol. It is suggested that experimentally identified Z{Cu(II)O] or Z[Cu(II)(OH)] are those sites that provide a homolytic cleavage of the methane C-H bond to yield surface bound methoxy species and/or methanol molecule, the possibility that has been recently justified with density functional theory (Kulkarni et al. Catal. Sci. Technol. 2018, 8, 114). The comparison of the amount of the surface methoxy intermediates formed and the number of different Cu(II) sites present in the zeolite allowed us to conclude the involvement of Z(2)Cu(II) sites in methane C-H bond activation. The mechanism of methane activation on Z(2)Cu(II) sites has been proposed. It includes two steps: (1) the formation of the molecular complex of methane with Z(2)Cu(II); (2) heterolytic dissociation of the polarized C-H bond affording surface copper(II) hydride and methoxy species, both bound to zeolite framework Si-O--Al sites.