  We report 125Te-NMR studies on a newly discovered heavy fermion
superconductor UTe2. Using a single crystal, we have measured the 125Te-NMR
Knight shift K and spin-lattice relaxation rate 1/T1 for fields along the three
orthorhombic crystal axes. The data confirm a moderate Ising anisotropy for
both the static (K) and dynamical susceptibilities (1/T1) in the paramagnetic
state above about 20 K. Around 20 K, however, we have observed a sudden loss of
NMR spin-echo signal due to sudden enhancement of the NMR spin-spin relaxation
rate 1/T2, when the field is applied along the easy axis of magnetization (=a
axis). This behavior suggests the development of longitudinal magnetic
fluctuations along the a axis at very low frequencies below 20 K.
