It is shown that several (single-mode) models (PTT, XPP) are basically special cases of the general network model. The XPP model [J. Rheol. 45 (2001) 823] is shown to give an identical response to a PTT model at high elongational rates, but the models differ in shear flow at high shear rates. The Giesekus term in the XPP model has practically no effect at any deformation rate except the generation of a second normal stress difference at small shear rates. The possibility of tailoring the shear flow response at high shear rates is explored. The results for the models are also given to show the effect of branching on the response in both transient and steady flows-elongation, shear, planar elongation and biaxial deformation. Finally, the fitting of data with multi-mode models is investigated. (C) 2003 Elsevier B.V. All rights reserved.