  We report experimental results of ^{75}As and ^{139}La nuclear magnetic
resonance (NMR) in the iron-based layered La(O_{1-x}F_{x})FeAs (x= 0.0, 0.04
and 0.11) system. In the undoped LaOFeAs, 1/T_1 of ^{139}La exhibits a distinct
peak at T_N ~ 142 K below which the spectra become broadened due to the
internal magnetic field attributed to an antiferromagnetic (AFM) ordering. In
the 4% F-doped sample, 1/T_1T exhibits a Curie-Weiss temperature dependence
down to 30 K, suggesting the development of AFM spin fluctuations with
decreasing temperature. In the 11% F-doped sample, in contrast, pseudogap
behavior is observed in 1/T_1T both at the ^{75}As and ^{139}La site with a gap
value of ~172 K. The spin dynamics vary markedly with F doping, which is
ascribed to the Fermi-surface structure. As for the superconducting properties
for the 4% and 11% F-doped samples, 1/T_1 in both compounds does not exhibit a
coherence peak just below T_c and follows a T^3 dependence at low temperatures,
which suggests unconventional superconductivity with line-nodes. We discuss
similarities and differences between La(O_{1-x}F_{x})FeAs and cuprates, and
also discuss the relationship between spin dynamics and superconductivity on
the basis of F doping dependence of T_c and 1/T_1.
