We present asymptotic Cosserat rod and string models for the simulation of slender viscous jets. In the set-up of rotational stationary spinning we examine the models with respect to their applicability/validity and efficiency. The string models are asymptotic limits of the rod in terms of a vanishing slenderness parameter. They consist of smaller systems of equations, but as a result of a singular asymptotic perturbation their applicability is restricted to certain parameter regimes – in contrast to the more complex and hence superior Cosserat rod. We investigate the existence regimes of two string models that differ in the closure conditions and determine their transition hyperplane numerically. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)