We present a theory for the dynamics of excitons in molecular aggregates in presence of polaronic effects caused by a strong coupling to an intramolecular vibration. Transitions between exciton states are assumed to occur by weak coupling to low-energy acoustic phonons. The theory can describe measurements of the polarization anisotropy decay of helical aggregates of oligo(p-phenylene-vinylene) derivatives in solution. The fitted cut-off frequency of the acoustic phonons agrees well with an estimate of the Debye frequency of the solvent. The inclusion of polaronic effects leads for long times to a slower, but for short times to a faster exciton dynamics. (C) 2012 Elsevier B. V. All rights reserved.