Recently, it has been shown that under pressure, unexpected and counterintuitive chemical compounds become stable. Laser shock experiments (A. Rode, unpublished) on alumina (Al2O3) have shown non-equilibrium decomposition of alumina with the formation of free Al and a mysterious transparent phase. Inspired by these observations, we have explored the possibility of the formation of new chemical compounds in the system Al-O. Using the variable-composition structure prediction algorithm USPEX, in addition to the well-known Al2O3, we have found two extraordinary compounds Al4O7 and AlO2 to be thermodynamically stable in the pressure ranges 330-443 GPa and above 332 GPa, respectively. Both of these compounds at the same time contain oxide O2- and peroxide O22- ions, and both are insulating. Peroxo-groups are responsible for gap states, which significantly reduce the electronic band gap of both Al4O7 and AlO2.