AbstractAccurate measurements of stress relaxation after steady‐state flow have been carried out, in the Newtonian flow region, for a polystyrene and a poly(methyl methacrylate) melt, with a cone‐and‐plate rotational rheometer. From the stress relaxation σ(t) versustcurves the relaxation spectraHwere calculated by means of the first approximation equation:\documentclass{article}\pagestyle{empty}\begin{document}$ H = - ({1 \mathord{\left/ {\vphantom {1 {\dot \gamma t)d\sigma {{(t)} \mathord{\left/ {\vphantom {{(t)} d}} \right. \kern-\nulldelimiterspace} d}}}} \right. \kern-\nulldelimiterspace} {\dot \gamma t)d\sigma {{(t)} \mathord{\left/ {\vphantom {{(t)} d}} \right. \kern-\nulldelimiterspace} d}}}\ln t $\end{document}. The shear stress–shear rate curves, σ versus\documentclass{article}\pagestyle{empty}\begin{document}$ {\dot \gamma } $\end{document}were also measured, in large ranges of shear rates, for the same melts, and from these data the relaxation spectraHwere obtained by means of equations given by Faucher and Ferry. The Faucher equation,\documentclass{article}\pagestyle{empty}\begin{document}$ H = - \dot \gamma ^2 d{\sigma \mathord{\left/ {\vphantom {\sigma d}} \right. \kern-\nulldelimiterspace} d}\dot \gamma ^2 $\end{document}, has been found to give results which compare satisfactorily with those obtained from the first approximation equation. It has been found that the Ferry equation has to be modified for comparable