We propose two schemes for generating Greenberger-Horne-Zeilinger and W states of three distant atoms. In the present schemes, the atoms are individually trapped in three spatially separated optical cavities coupled by two optical fibres. Performing an adiabatic passage along dark states, the population of cavities and fibres excited is negligible under certain conditions. In addition, the spontaneous decay of atoms is also efficiently suppressed based on our proposals. Furthermore, the discussion about the entanglement fidelity is given and we point out that our schemes work robustly with small fluctuations of experimental parameters.
