We measured quasielastic neutron spectra (0.2 < Q < 1.8 Å −1) with a resolution of 13 μeV (HWHM) for 56% H 2O-hydrated powder samples of the tripeptide glutathione, using a new pulsed-source backscattering instrument with considerable potential for advancing work on biomolecular dynamics. Both window-integrated intensities and spectrally resolved dynamic structure factors were determined for temperature sequences going down from 300 to 50 K and then up again to 300 K at the same points. We discuss four features of the results obtained: (a) The slow increase of proton mobilities from 50 K towards 250 K; (b) the properties of a sharp dynamic transition near 260 K; (c) the onset of quasielastic broadenings around 270 K; (d) small T and Q dependent changes observable in up minus down difference spectra.