It has long been known that the behavior of HDPE (high density polyethylene) and LDPE (low density polyethylene) in various polymer processing operations. is fundamen-tally different from each other. For example. in melt spinning, the critical draw-down ratio (r_c) causing the onset of draw resonance, has much smaller values for HDPE than those for LDPE, and also the effect of the material relaxation time (λ) on draw resonance is opposite in HDPE as compared to LDPE. In this paper, we show that these two different modes of the behavior of HDPE and LDPE can be predicted by using the Hyun''s draw resonance theory on the spinning of convected Maxwell fluids with the White''s strain-rate dependent relaxation time model. The Hyun''s kinematical wave theory of draw resonance has recently been confirmed to be correct by the numerical calculation of the pertinent partial derivatives in the (x,t) coordinate system. The results of these numerical simulation studies will be reported elsewhere.