  Co nuclear magnetic resonance (NMR) and nuclear quadrupole resonance (NQR)
studies were performed in the recently discovered UCoGe, in which the
ferromagnetic and superconducting (SC) transitions were reported to occur at
$T_{\rm Curie} \sim 3$ K and $T_S \sim 0.8$ K (N. T. Huy {\it et al.}, Phys.
Rev. Lett. {\bf 99} (2007) 067006), in order to investigate the coexistence of
ferromagnetism and superconductivity as well as the normal-state and SC
properties from a microscopic point of view. From the nuclear spin-lattice
relaxation rate $1/T_1$ and Knight-shift measurements, we confirmed that
ferromagnetic fluctuations which possess a quantum critical character are
present above $T_{\rm Curie}$ and the occurrence of ferromagnetic transition at
2.5 K in our polycrystalline sample. The magnetic fluctuations in the normal
state show that UCoGe is an itinerant ferromagnet similar to ZrZn$_2$ and
YCo$_2$. The onset SC transition was identified at $T_S \sim 0.7$ K, below
which $1/T_1$ of 30 % of the volume fraction starts to decrease due to the
opening of the SC gap. This component of $1/T_1$, which follows a $T^3$
dependence in the temperature range of $0.3 - 0.1$ K, coexists with the
magnetic components of $1/T_1$ showing a $\sqrt{T}$ dependence below $T_S$.
  From the NQR measurements in the SC state, we suggest that the self-induced
vortex state is realized in UCoGe.
