Within the framework of the one-dimensional S = 1/2 Heisenberg model with a
next-nearest-neghbor antiferromagnetic interaction, a theory of the copper
spin-lattice relaxation in the uniform state of the spin-Peierls compound
CuGeO3 is presented. The main contribution to the relaxation rate at interm
ediate and high temperatures is due to the spin diffusive long-wave process
es. A comparison of our results with experimental data shows that the theor
y is able to reproduce the main features of the temperature dependence of t
he copper relaxation rate.