Abstract: Ab initio calculations within the density functional theory formalism are performed to investigate the stability and electronic properties of fluorinated bilayer graphene (bilayer fluorographene). A comparison is made to previously investigated graphane, bilayer graphane, and fluorographene. Bilayer fluorographene is found to be a much more stable material than bilayer graphane. Its electronic band structure is similar to that of monolayer fluorographene, but its electronic band gap is significantly larger (about 1 eV). We also calculate the effective masses around the Gamma-point for fluorographene and bilayer fluorographene and find that they are isotropic, in contrast to earlier reports. Furthermore, it is found that bilayer fluorographene is almost as strong as graphene, as its 2D Young's modulus is approximately 300 N m(-1).