A general transformation procedure (GTP) for viscoelastic differential constitutive equations is proposed. This procedure is devised to transform a differential model (e.g. Oldroyd-B, White-Metzner (WM) and Phan-Thien-Tanner (PTT)) into another model which has just one differential equation to be solved. The resulting model is suitable for three-dimensional and time-dependent flows. A new generalized objective time derivative is employed in the procedure, lending important features to the transformed model. For example, for the case of the Oldroyd-B model, the transformed model is capable of predicting non-zero second normal stress differences. Calculations of the stress field have been performed with an Oldroyd-B based GTP model (the GTP[OldB] model) for a 4:1 contraction plane flow. The results obtained have been analyzed with the aid of a flow-type classifier, and were found to be in good agreement with the ones obtained with the original model. (C) 2003 Elsevier Science B.V. All rights reserved.