Progress was achieved in the last years in the development of multilayer mirrors used in storage ring Free Electron Lasers (FEL) operating in the vacuum ultraviolet spectral range. Based on dense oxide coatings deposited by Ion Beam Sputtering, a stable lasing at 190 nm was demonstrated. The extension towards shorter wavelengths had to overcome severe problems connected to the radiation resistance and the necessary reflectivity of the resonator mirrors. In this context, radiation resistance can be considered as the ability of the mirror materials to withstand the high power laser radiation and the intense energetic background radiation generated in the synchrotron source. The bombardment with high energetic photons leads to irreversible changes and a coloration on the specimen. Reflectivity requirements can be evaluated from the tolerable losses of FEL systems. At ELETTRA FEL the resonator mirror reflectivity must be above 95 \%. Evaporated fluoride multilayer mirrors provide sufficient reflectivity, but they do not exhibit an adequate radiation resistance. Pure oxide multilayers show a sufficient radiation resistance, but they cannot reach the necessary reflectivity below 190 nm. A successful approach combines evaporated fluoride multilayer stack with a dense protection layer of silicon dioxide deposited by Ion Beam Sputtering. Such mirror systems were produced reaching a reflectivity of approximately 99 \% at 180 nm. Lasing in the storage ring FEL at ELETTRA was realised in the range between 176 - 179 nm. The mirror reflectivity shows only a slight degradation after lasing, which could be fully restored after the lasing experiment.