We study the time evolution of the one-dimensional random-bond transverse I
sing model with four-spin interactions. We calculate the time-dependent cor
relation function as well as the longitudinal relaxation function of the in
finite chain. We analyze how the presence of disorder affect the dynamical
behavior of the system in comparison with the pure model. We find that the
main effect of disorder is to produce a crossover from a central mode to a
collective-mode type of dynamics, as the concentration of weaker bonds is e
nhanced. Such crossover is also present in the case of an increase in bond
dilution.