  A theoretical interpretation is given to recent proton spin relaxation-time
(T_1) measurements on NiCu(C_7H_6N_2O_6)(H_2O)_3$\cdot$2H_2O, which is an ideal
one-dimensional ferrimagnetic Heisenberg model system of alternating spins 1
and 1/2. The relaxation rate T_1^{-1} is formulated in temrs of the spin-wave
theory and is evaluated by the use of a quantum Monte Carlo method.
Calculations of the temperature and applied-field (H) dependences of T_1^{-1}
are in total agreement with the experimental findings. T_1 behaves as
$T_1^{-1}\propto H^{-1/2}$, which turns out an indirect observation of the
quadratic dispersion relations dominating the low-energy physics of quantum
ferrimagnets.
