  The temperature dependence of the site-dependent nuclear spin relaxation time
T_1 around vortices is studied in s-wave and d-wave superconductors.Reflecting
low energy electronic excitations associated with the vortex core, temperature
dependences deviate from those of the zero-field case, and T_1 becomes faster
with approaching the vortex core. In the core region, T_1^{-1} has a new peak
below T_c. The NMR study by the resonance field dependence may be a new method
to prove the spatial resolved vortex core structure in various superconductors.
