After passing through an extruder, a small amount of degradation normally occurs in the high molecular weight tail of a broadly distributed polymer sample. This small amount of degradation could dramatically affect the polymer viscoelastic properties. It is difficult to detect this type of degradation by using conventional analytical methods, such as high temperature size exclusion chromatography. An investigation of this type of degradation in a broadly distributed polyethylene sample was accomplished by using high-temperature dynamic light-scattering (HTDLS). We have shown that the measured line-width (or the translational diffusion coefficient) distribution in the HTDLS is proportional to M(alpha) with alpha = 3.580 +/- 0.005, so that the HTDLS is a very sensitive technique for detecting a very small amount of degradation in the high molecular weight tail. Another advantage of using the HTDLS is that the study does not introduce further stress or perturbation into the sample. In this study, we also investigated the thermal degradation of the polyethylene sample in trichlorobenzene at high temperatures. We found that the polyethylene sample after the extrusion undergoes a thermal degradation more easily.