The avoided-level-crossing relaxation of a polarized muon spin-label was used to investigate the reorientational dynamics of muonated cyclohexadienyl radicals in NaZSM-5 with SiO2/Al2O3 ratios of 670 and 900 and loadings of one and two benzene molecules per unit cell. It was found that on a critical time scale of about 50 ns the radical performs fast uniaxial rotation about the axis perpendicular to the molecular plane. Superimposed on this there is a two-site jump motion between two orientations that differ by an angle of 110 degrees and 1.0 kJ mol(-1) in energy. This causes increasing averaging of the orientations above 50 K. It is particularly extensive but still not isotropic in a temperature range between 200 and 450 K. Below 50 K, the uniaxial rotation slows down below the critical time scale of the experiment, and below 20 K any motion is frozen. It is suggested that such a high reorientational mobility is possible only for the radicals occupying sites at the channel intersections. Above ca. 450 K, the reversible appearance of new broad spectral features suggests that new sites with much lower mobility become thermally accessible. These may be located inside the channels.