The effect of thixotropy on the two-dimensional spreading of a sessile drop is modelled using lubrication theory. Thixotropy is incorporated by the inclusion of a structure parameter, lambda, measuring structure build-up governed by an evolution equation linked to the droplet micromechanics. A number of models are derived for lambda coupled to the interface dynamics; these range from models that account for the cross-stream dependence of lambda to simpler ones in which this dependence is prescribed through appropriate closures. Numerical solution of the governing equations show that thixotropy has a profound effect on the spreading characteristics; the long-time spreading dynamics, however, are shown to be independent of the initial structural state of the droplet. We also compare the predictions of the various models and determine the range of system parameters over which the simple models provide sufficiently good approximations of the full, two-dimensional spreading dynamics. (C) 2017 The Authors. Published by Elsevier B.V.