  We study the critical dynamics of crystals which undergo a second-order phase
transition from a high-temperature normal phase to a structurally
incommensurate (IC) modulated phase. We give a comprehensive description of the
critical dynamics of such systems, e.g. valid for crystals of the A_2BX_4
family. Using an extended renormalization scheme, we present a framework in
which we analyze the phases above and below the critical temperature T_I. Above
T_I, the crossover from the critical behavior to the mean-field regime is
studied. Specifically, the resulting width of the critical region is
investigated. In the IC modulated phase, we consider explicitly the coupling of
the order parameter modes to one-loop order. Here the Goldstone anomalies and
their effect on measurable quantities are investigated. We show their relation
with the postulated phason gap. While the theory can be applied to a variety of
experiments, we concentrate on quadrupole-perturbed nuclear magnetic resonance
(NMR) experiments. We find excellent agreement with these dynamical
measurements and provide answers for some questions that arose from recent
results.
