  The relationship for Pulsed-Field-Gradient NMR between the amplitude $I(t)$
of the spin echo and the molecular displacement ${\bf X}(t)$ is examined.
$I(t)$ of a single species in a simple solution is determined by the
mean-square displacement $\bar{X(t)^{2}}$. With polydisperse species, or
molecular probes in complex fluids showing memory effects, $I(t)$ in general
includes large contributions from all higher even moments $\bar{X(t)^{2n}}$.
Conditions under which the NMR signal is indeed determined by the molecular
mean-square displacement are noted. A diagnostic that sometimes identifies when
these conditions are not met is presented.
