Effective elongational viscosities were measured for high- and low-density polyethylene samples using a capillary rheometer fitted with semihyperbolic dies. These dies establish a purely elongational flow field at constant elongational strain rate. The effective elongational viscosities were evaluated under the influence of the process strain rate, Hencky strain, and temperature. Enthalpy and entropy changes associated with the orientation development of semihyperbolic-processed melts were also estimated. The results showed that elongational viscosities were primarily affected by differences in the weight-average molecular weight rather than in the degree of branching. This effect was process-strain-rate- as well as temperature-dependent. An investigation of the melt-pressure relaxation and the associated first decay time constants revealed that with increasing strain rate the molecular field of the melt asymptotically gained orientation in approaching a limit. As a result of this behavior, molecular uniqueness became much less distinct at high process strain rates, apparently yielding to orientation development and the associated restructuring of the melt's molecular morphology.