With regard to possible involvement of zeolite Brønsted acid sites (BAS) in the activation of methane molecules for methane transformation to methanol, the effect of different Cu(II) species loaded in the zeolite on the kinetic parameters of the reaction of H/D hydrogen exchange of the alkane with BAS of Cu-modified ZSM-5 zeolites has been investigated with 1H MAS NMR in situ at 533-563 K. It is found that the acceleration of the H/D exchange by 1 order of magnitude occurs for zeolite containing Cu2+ cations (Z2Cu(II) sites) or [Cu3(μ-O)3]2+ oxo-clusters (Z2[Cu3(μ-O)3] sites) compared to pure H-form zeolite. It is thus inferred that both Z2Cu(II) and Z2[Cu3(μ-O)3] sites exhibit the promoting effect of copper on the activation of methane C-H bonds by BAS. Acceleration of the H/D exchange is rationalized by the change of the mechanism of the exchange accepted for the H-form zeolites for the mechanism that involves the formation of a transient molecular complex of methane with Cu(II) species, preceding the H/D exchange reaction. The formation of the complex of methane with both Z2Cu(II) and Z2[Cu3(μ-O)3] sites is confirmed by DRIFTS. BASs with a higher strength than in H-ZSM-5, generated in the zeolite at copper loading, are concluded to not be responsible for the H/D exchange reaction acceleration.