  We report ^59Co-NMR measurements in UCoAl where a metamagnetism occurs due to
enhancement of ferromagnetism by magnetic field. The metamagnetic transition
from a paramagnetic (PM) state to a ferromagnetic state is a first order
transition at low temperatures, but it changes to a crossover at high
temperatures on crossing the critical end pint (CEP) at T_CEP ~ 12 K. The
contrasting behavior between the relaxation rates 1/T_1 and 1/T_2 suggests that
the longitudinal magnetic fluctuation of U moment is strongly enhanced
especially near the CEP. A wide diffusion of the fluctuation from the CEP can
be confirmed even in the PM state where the magnetic transition does not occur.
