We present results from molecular dynamics computer simulations of the dynamic properties of amorphous material derived from zeolite ZSM-5, in particular secondary relaxations for temperatures below the critical temperature. We observe local jumps where groups of atoms move collectively. At low temperatures the relaxations comprise mainly of one-dimensional chains of atoms. The dimensionality of the relaxing centers increases with the temperature due to side branching. Both the displacement vector and the number of atoms participating in the jumps increase with temperature. The possibility of having reversible jumps decreases with increasing temperature due to a strong drop in the potential energy during aging. There exist very prominent peaks in the van Hove correlation functions as a manifestation of the hopping processes. The dynamics of the oxygen atoms is found to be more heterogeneous than those of the silicon atoms.