Ethylene has been established to form stable π-complexes with Ag+ cations in Ag-modified zeolite H-ZSM-5 (Ag/H-ZSM-5), which strongly affect the reactivity of ethylene on this catalyst. With the aim of revealing the catalytic and adsorptive properties of Ag+ cations in Ag/H-ZSM-5, a characterization of the mobility of ethylene π-complex, located in the zeolite pores, has been performed with 2H solid-state NMR spectroscopy. Ethylene molecules were established to remain bound to the Ag+ cations at temperatures up to 556 K. In the bound state, ethylene exhibits a 2H NMR line shape typical for anisotropic motions. It is inferred that being adsorbed on Ag+ cation, ethylene molecule is involved in two internal rotations about its symmetry axes: along the C2 axis aligned with the C=C bond and about the second C′2 axis orthogonal to the molecule plane. The first rotation occurs with the rate k1 of 10-40 kHz and activation barrier E1 = 2.3 kJ mol-1, while the second motion occurs with the rate k2 of 10-400 kHz and E2 = 4.7 kJ mol-1. The latter motion is faster than the former one. Both motions occur by four-site jump exchange mechanism. When methane is coadsorbed on the zeolite, the dynamical picture becomes different within two different temperature regions, with T ≤ 392 K and T > 392 K. Below 392 K, the rotation mechanism is similar to that without methane coadsortion. However, the barrier for the rotation about the C′2 axis increases (E2II = 7.4 kJ mol-1), which is evidence for the methane interaction with the ethylene π-complex. At temperatures as high as 392 K, the 2H NMR line shape of adsorbed ethylene becomes typical for isotropic-like motion. The barrier of the motion, E = 25 kJ mol-1, is accounted for by involvement of ethylene in the presence of methane in some isotropic or translational motions. At T ≥ 491 K, the line shape analysis reveals an H/D exchange between C2D4 and CH4.