The polymer relaxation dynamic of a sample, stretched up to the stress hardening regime, is measured, at room temperature, as a function of the strain $lambda$ for a wide range of the strain rate $dotgamma$, by an original dielectric spectroscopy set up. The mechanical stress modies the shape of the dielectric spectra mainly because it affects the dominant polymer relaxation time $tau$, which depends on $lambda$ and is a decreasing function of $dotgamma$. The fastest dynamics is not reached at yield but in the softening regime. The dynamics slows down during the hardening, with a progressive increase of $tau$. A small inuence of $dotgamma$ and $lambda$ on the dielectric strength cannot be excluded.