Small-angle neuron scattering has been applied to mixtures of deuteropolyethylene terephthalate and polyethylene naphthalene-2,6-dicarboxylate that have been transesterified at temperatures of 543-573 K for a range of times. The change in scattering cross section has been analysed to provide values of the rate constants and, hence, the activation energies for the reaction. Excellent agreement for the rate constants is obtained with results reported by using NMR to analyse the reacted mixtures. Activation energies have been obtained as a function of the polyethylene terephthalate content of the mixtures and, additionally, for the transesterification in polyethylene naphthalene 2,6-dicarboxylate alone obtained from small-angle neutron scattering. The activation energy values range from 93 kJ mol(-1) for pure polyethylene naphthalene-2,6-dicarboxylate to 160 kJ mol(-1) for pure polyethylene terephthalate, with a distinct composition dependence being evident for polyethylene terephthalate weight fractions below 0.5.