The dynamic behavior of a system undergoing a co-operative Jahn-Teller structural transition is investigated. Coupling to both acoustic and optic modes are considered. Particular emphasis is placed on the low frequency response. In addition to the peaks in the dynamic structure factor corresponding to the soft acoustic mode, a central component is obtained, the width of which goes to zero as the transition temperature is approached. Unlike other transitions for which a central component has been observed, the width of the central peak for Jahn-Teller transitions such as that in TmVO4 may be sufficiently wide to allow a direct observation of the narrowing by neutron scattering or other techniques. © 1974, Taylor … Francis Group, LLC. All rights reserved.