Nuclear spin-lattice relaxation in paramagnetic systems is treated usi
ng the classic expression for transition probability between the coupl
ed electron and nuclear spin states. The rate equations governing the
incoherent occupancies of these states are solved analytically (where
possible) and numerically (where not) to construct the relaxation func
tion for the nuclear spin. The method is illustrated for muonium, and
the muonium-substituted molecular radicals, for the case of perturbati
on due to fluctuation of the local field, i. e. modulation of the inte
raction with a third spin. A slight departure from single exponential
behaviour is demonstrated for slow fluctuations.