The necking behavior in the high-speed melt-spinning process of poly(ethylene terephthalate) (PET) was analyzed using a mathematical simulation under a nonisothermal condition. A constitutive model into which the strain-rate dependence of viscosity and the strain-hardening effect are incorporated was used. Based on the simulated results, the cause of a local reduction of apparent viscosity was found to be due mainly to high strain rate. Also the onset of crystallization, if it occurred, was found to happen near the end of the neck. In addition, with no crystallization involved, the necking can still occur. The deformation process in high-speed spinning of PET was found to consist of two regions along the spin line: a Newtonian flow region and a rubberlike deformation region. The necking behavior is discussed here in terms of strain-rate sensitivity and strain-hardening parameter. As a result, a criterion for the onset of stable necking has been obtained. The necking behavior does not seem to be essentially different from that in cold drawing. (C) 2000 John Wiley & Sons, Inc.