To elucidate the superconducting gap structure and the influence of rattling motion on quasiparticle dynamics in the superconducting state of KOs2 O6, thermal conductivity and microwave surface impedance were measured at low temperatures. The magnetic field dependence of thermal conductivity at the lowest temperature and the temperature dependence of penetration depth strongly indicate a fully gapped superconductivity in KOs2 O6. The quasiparticle scattering time is strongly enhanced in the superconducting state, indicating a strong electron-electron inelastic scattering in the normal state. These results highlight that KOs2 O6 is unique among superconductors, which is characterized by the coexistence of fully gapped superconductivity and strong electron correlations. © 2008 Elsevier Ltd. All rights reserved.