This paper describes the necking phenomena of undrawn polyester fibers in stretching under various conditions in the vieinity of glass transition temperature. Neck ungle is used as a parameter whichexpresses the characteristics of the necking geometry. This parameter means the angle between the direction of the necking shoulder and the fiber axis. The neck angle is very sensitive to the temperature and propagation rate. The plots of necking angle against the propagation rate abtained at different temperatures cone be superimposed to a master curve by shibting the plot along the rate axis. The shift factor log aT-temperature relationship agrees quite well with the WLF equation, with exception at temperatures lower than the apparent Tg under external force.The necking phenomena are characterized by the necking draw ratio, the necking tension and the birefringence of the necking region. These factors depend a priori on the neck angle irrespective of the drawing condition.Finally, it must be recognized that the necking is a relaxation phenomena within a large wale of temperature and therefore the necking always occurs at temperatures lower than Tg even in the very low rate of stretching.