The superconducting properties of two -pyrochlore oxides, CsOs 2 O 6 and RbOs 2 O 6 , are studied by thermodynamic and transport measurements using high-quality single crystals. It is shown that the character of superconductivity changes systematically from weak coupling for CsOs 2 O 6 to moderately strong coupling for RbOs 2 O 6 , and finally to extremely strong coupling with BCS-type superconductivity for KOs 2 O 6 , with increasing T c . Strong-coupling correction analyses of the superconducting properties reveal that a low-energy rattling mode of the alkali metal ions is responsible for the mechanism of the superconductivity in each compound. The large enhancement of T c from Cs to K is attributed to the increase in the electron-rattler coupling with decreasing characteristic energy of the rattling and with increasing anharmonicity. The existence of weak anisotropy in the superconducting gap or in the electron-rattler interactions is found for the Cs and Rb compounds.