A number of models are available to describe the rheological behaviour of associative polymers. Model evaluation has most often been limited to the linear properties and to a qualitative prediction of the characteristic shear thickening at intermediate shear rates. Several other nonlinear features of associative behaviour have, however, been identified. These include failure of the Cox-Merz analogy and an unusual response in nonlinear stress relaxation, large amplitude oscillatory flow and in superposition flows. Here, experimental results for such experiments are compared with the predictions of a transient network model, i.e. the Vaccaro-Marrucci model [J. Non-Newtonian Fluid Mech. 92 (2000) 261], which has only a single adjustable parameter to describe nonlinear behaviour. It is shown that the various nonlinearities are well predicted qualitatively. The only deviation is a substantial overprediction of the critical strain or strain rate for the onset of these nonlinearities. The effect of changing the value of the model parameters and of relaxing the model assumptions on the predictions is investigated. The results suggest that the presence of a small number of highly stretched chains could be responsible for the observed deviation from the experimental data. (C) 2004 Elsevier B.V. All rights reserved.