A peculiar deformation in the threadline region resembling the "necking" associated with cold drawing of some metals and many polymeric fibers is observed when polyethylene terephthalate (PET) and other semicrystalline polymers are melt-spun at high speeds. This phenomenon is often referred to as the "neck"-like deformation. Perez and Lecluse were the first to report the "neck"-like deformation in the high-speed spinning of PET. Thus far, it has been observed that necking is seen only for polymers which crystallize in the threadline. It is generally believed that the occurrence of necking is in some way associated with the crystallization process. It is still not known whether crystallization initiates necking or vice versa. In our work, we have conducted an analysis of the necking phenomenon based on a geometric description of the neck and applied it to the basic melt-spinning equations to understand what situations can lead to neck formation in the high-speed spinning of fibers. In our analysis, a decrease in viscosity has been proven as a necessary condition for neck formation. A negative viscosity gradient implies that just before the neck region, the viscosity suddenly decreases. In a typical fiber spinning process, normally the reverse process happens: the polymer viscosity increases exponentially along the spinning threadline as the extrudate is transformed from a melt to a solid filament. Our analysis provides a mechanism for rationalizing the observed "neck"-like phenomenon in highspeed spinning by invoking the importance of radial position and availability of released heat of crystallization from crystallization occurring in the skin region, to reduce the viscosity of the fiber core. It is not speed alone which affects threadline crystallization. Of equivalent importance is the existence of favorable thermal conditions in the threadline.