To study how highly magnetized liquids behave in NMR experiments, we have p
erformed low-field NMR on laser-polarized liquid Xe-129, with nuclear polar
ization of up to 6%. Contrary to conventional NMR results, we find that ins
tabilities develop after a large pulse, leading to an unexpectedly abrupt d
ecay of the signal. In contrast, the NMR spectrum after a small pulse colla
pses to a series of unusually sharp lines (spectral clustering), whose widt
hs correspond to precession lifetimes longer than a half minute. We discuss
the key role of long-range dipolar coupling in such spin dynamics.