  We present calculations of the rate of planar Cu spin lattice relaxation in
the mixed state of YBaCuO due to (i) vortex vibrations and (ii) electron
spin-flip scattering. We emphasize that both mechanisms give position dependent
rates due to the presence of vortices, and hence the magnetization recovery is
characterized by a distribution of rates. We conclude that relaxation by vortex
vibrations is too slow to be a significant factor in this material. Using a
semiclassical model of Doppler shifted d-wave quasiparticles with a linear
dispersion around the nodes, our calculation of the relaxation rate from
electron spin-flip scattering shows partial agreement with experiment.
