We study, through direct numerical simulation and asymptotic analysis, the evolution and break-up of jets of viscoelastic fluids of Giesekus and FENE-P type. In both cases, the jet diameter decreases linearly with time close to break-up in the inertial regime and the profiles are self-similar asymmetric. Sufficiently far from break-up, an inertialess regime develops with self-similar symmetric features. We deduce and verify numerically the scaling laws obeyed by the jet during the evolution. In particular, we describe the self-similar nature of the neck between thinning filaments and drops. (C) 2004 Elsevier B.V. All rights reserved.