Quasielastic neutron scattering was applied to investigate the protonic motion in water-doped Ba[Ca0.39Nb0.61]O-2.91 between 5 and 700 K. The backscattering spectra in the mu eV-region for small scattering vectors Q lead to the protonic self-diffusion constant. The results were compared with measurements of the electrical conductivity. At larger Q, the spectra reveal two superimposed quasielastic components probably related to two groups of jump rates. Low resolution measurements indicate a rapid rotation of the hydroxyl groups.