The polymer relaxation dynamic of a sample, stretched up to the stress hardening regime is measured at room temperature as a function of the strainλ for a wide range of the strain rate ˙γ using an original dielectric spectroscopy set up. The mechanical stress modifies the shape of the dielectric spectra mainly because it affects the dominant polymer relaxation time τ, which depends on λ and is a decreasing function of ˙γ. 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 τ. A small influence of ˙γ and λ on the relative dielectric strength cannot be excluded.