We develop a theory of critical dynamics for the rotations of the BO6 octahedra in ABO3 perovskites at T Tc. Given a "conventional" soft mode, we derive, using the third longtime approximation of Mori's continued-fraction representation, an approximate expression for the dynamic order-parameter form factor. This description leads, close to Tc, to the correct three-pole structure around ω=0, including the central peak and the resonances of the conventional soft mode. The central peak is predicted to appear whenever the conventional soft-mode frequency and the isothermal phonon frequency differ considerably. This gives support to Feder's prediction. Given a soft acoustic mode, the theory also accounts for a central peak, as does the phenomenological theory of Shirane and Axe. Our theory, which leads by construction to a correct three-pole structure around ω=0, justifies and clarifies the phenomenological expressions for the dynamic order-parameter form factor, as proposed by Schwabl and Shirane and Axe. © 1973 The American Physical Society.