  We report on Sb nuclear-quadrupole-resonance (NQR) study in
filled-skutterudite compounds (Pr_1-xLa_x)Os_4Sb_12. The Sb-NQR spectra have
split into two sets, arising from different Sb_12 cages containing either Pr or
La, which enables us to measure two kinds of nuclear spin-lattice relaxation
time T_1^Pr and T_1^La. In the normal state, the temperature (T) dependence of
1/T^Pr_1T showed almost the same behavior as that for PrOs_4Sb_12 regardless
of. In contrast, 1/T^La_1T markedly decreases with increasing La concentration.
In the superconducting state for x=0.05 and 0.2, 1/T_1^Pr exponentially
decreases down to T=0.7 K with no coherence peak below T_c as well as in
PrOs_4Sb_12. A remarkable finding is that the residual density of states at the
Fermi level below T_c is induced by La substitution for Pr. These results are
proposed to be understood in terms of a multiband-superconductivity model that
assumes a full gap for part of the FS and the presence of point nodes for a
small 4f^2-derived FS inherent in PrOs_4Sb_12. For x=0.8 and 1,1/T^La_1
exhibits a coherence peak and the nodeless energy gap characteristic for
weak-coupling s-wave superconductors. With increasing Pr content, T_c and the
energy gap increases. The novel strong-coupling superconductivity in
PrOs_4Sb_12 is inferred to be mediated by the local interaction between
4f^2-derived crystal-electric-field states with the electric quadrupole degree
of freedom and conduction electrons. This coupling causes a mass enhancement of
quasi-particles for a part of FS and induces a small FS, which is responsible
for point nodes in the superconducting gap function. Note that the small FS
does not play any primary role for the strong-coupling superconductivity in
PrOs_4Sb_12.
