The complex dynamical behavior of the disordered hydrogen atoms in the recently discovered cluster compounds Th6H7Br15 and Th6H5Br15 has been investigated by means of H-1 solid state NMR, Two different modes of motion can be identified, At temperatures above 250 K the spin-lattice relaxation is dominated by a thermally activated intercluster jump process with an activation energy of about 4200 K (360 meV), The emergence of this process results in an abrupt line narrowing of the NMR spectrum at 270 K. Down to the lowest measured temperature of 80 K a local intracluster mode is effective. The low-temperature proton spin-lattice relaxation time is analyzed on the basis of a first principle stochastic model for Th6H7Br15. A dynamically disordered and phonon assisted tunneling process is proposed for the low-temperature dynamics.