The steady‐flow viscosity&eegr;(&ggr;˙),the loss modulusG″(&ohgr;), and the storage modulusG′(&ohgr;) for five linear polyethylene melts (190°C) were measured using the Weissenberg rheogoniometer and the Instron rheometer. An excellent agreement was observed between the experimentalG′(&ohgr;) andG″(&ohgr;) values and those calculated from the relaxation spectrum obtained from&eegr;(&ggr;˙)using the relation&eegr;(&ggr;˙)=∫H(ln&tgr;)h(&thgr;)g(&thgr;)3/2&tgr;d ln&tgr;,  &thgr;=&ggr;˙&tgr;/2.Here, &ggr;˙ is the shear rate, &ohgr; is the radian frequency, and &tgr; is the relaxation time. The functionsg(&thgr;) andh(&thgr;) are expressed asg(&thgr;)=(2/&pgr;)[cot−1&thgr;+&thgr;/(1+&thgr;2)]  and  h(&thgr;)=(2/&pgr;)[cot−1&thgr;+&thgr;(1−&thgr;2)/(1+&thgr;2)2].No coordinate shift was required. An interative procedure was used in such an interconversion. The first approximation to the spectrumH1(ln&tgr;) was(2/&pgr;)[&eegr;(&ggr;˙)×&ggr;˙]and the corresponding viscosity was&eegr;1(&ggr;˙).The successive approximations were expressed by the equationHK(ln&tgr;)=HK−1(ln&tgr;)+p&ggr;˙[&eegr;(&ggr;˙)−&eegr;K−1(&ggr;˙)],wherep=2/&pgr; andK≥2. In all cases, only six iterations were required to achieve satisfactory convergence. The relaxation spectra so obtained from viscosity measurements at large shearing deformation were in excellent agreement with those calculated fromG″(&ohgr;) measured in oscillatory experiments carried at small deformation.