A new filament stretching rheometer has been constructed to measure the elongational viscosity of polymer melts at high temperatures. Two polymer melts, a LDPE and a LLDPE, were investigated with this rheometer. A constant elongational rate has been obtained by an iterative application of the Orr-Sridhar method for specification of the end-plate movement. Agreement has been found with linear viscoelastic measurements performed in shear. Hencky strains up to about 6 have been reached. Steady values of the viscosity have been sustained in some cases for about two Hencky strain units. (C) 2003 The Society of Rheology.