The dynamic spin susceptibility is calculated for the t-J model in the
paramagnetic phase using the memory function method in terms of the H
ubbard operators. A self-consistent system of equations for the memory
function is obtained in the mode-coupling approximation. Both itinera
nt hole excitations and localized spin fluctuations contribute to the
memory function. The spin dynamics have a diffusive character in the h
ydrodynamic limit; spin-wave-like excitations are regained in the high
-frequency region.