  We investigate the time-dependent Kondo effect in a single-molecule magnet
(SMM) strongly coupled to metallic electrodes. Describing the SMM by a Kondo
model with large spin S > 1/2, we analyze the underscreening of the local
moment and the effect of anisotropy terms on the relaxation dynamics of the
magnetization. Underscreening by single-channel Kondo processes leads to a
logarithmically slow relaxation, while finite uniaxial anisotropy causes a
saturation of the SMM's magnetization. Additional transverse anisotropy terms
induce quantum spin tunneling and a pseudospin-1/2 Kondo effect sensitive to
the spin parity.
