The growth kinetics of a system with spin-exchange dynamics has been invest
igated by means of computer simulations. These systems are used to simulate
diffusive processes and kinetic phenomena far away from equilibrium. As a
measure of growth we have studied the mean square displacement (<R-2> of ta
gged particles. It is found that <R-2>t(1-n) follows a sublinear time depen
dence, which is explained in terms of the changes of the distribution of at
oms between sites within the ordered region and sites of the domain boundar
ies. The time-dependence of the diffusion coefficient has been derived. The
analogies to the relaxation in disordered systems, such as in a:Si-H and i
n O/W(110), is discussed.