We discuss the novel superconducting characteristics and unusual normal-state properties of iron (Fe)-based pnictide superconductors REFeAsO$_{1-y}$ (RE=La,Pr,Nd) and Ba$_{0.6}$K$_{0.4}$Fe$_2$As$_2$($T_{c}=$ 38 K) by means of $^{57}$Fe-NMR and $^{75}$As-NQR/NMR. In the superconducting state of LaFeAsO$_{0.7}$ ($T_{c}=$ 28 K), the spin component of the $^{57}$Fe-Knight shift decreases to almost zero at low temperatures, which provide firm evidence of the superconducting state formed by spin-singlet Cooper pairing. The nuclear spin-lattice relaxation rates $(1/T_{1})$ in LaFeAsO$_{0.7}$ and Ba$_{0.6}$K$_{0.4}$Fe$_2$As$_2$ exhibit a $T^{3}$-like dependence without a coherence peak just below $T_{c}$, indicating that an unconventional superconducting state is commonly realized in these Fe-based pnictide compounds. All these events below $T_c$ are consistently argued in terms of an extended s$_{pm}$-wave pairing with a sign reversal of the order parameter among Fermi surfaces. In the normal state, $1/T_1T$ decreases remarkably upon cooling for both the Fe and As sites of LaFeAsO$_{0.7}$. In contrast, it gradually increases upon cooling in Ba$_{0.6}$K$_{0.4}$Fe$_2$As$_2$. Despite the similarity between the superconducting properties of these compounds, a crucial difference was observed in their normal-state properties depending on whether electrons or holes are doped into the FeAs layers. These results may provide some hint to address a possible mechanism of Fe-based pnictide superconductors.
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