We have measured the magnitude and temperature dependences of T2e and T1e in undoped polyacetylene. The T2e measurements and the determination of soliton diffusion rates from them are summarised. New T1e measurements on (CD)x and (CH)x at 9.5 GHz and 16.7 GHz are presented. These measurements are utilised to compute nuclear spin relaxation times, T1p, via the mechanism of nuclear spin diffusion to fixed paramagnetic impurities. It is shown that the results of this calculation agree with published NMR measurements at least as well as does the soliton diffusion model