The sesquioxides of molybdenum and tungsten have been reported as thin films or on surfaces as early as 1971, but the preparation of bulk materials and their crystal structures are still unknown up to the present day. We present a systematic ab initio approach to their possible syntheses and crystal structures applying complementary methods and basis-set types. For both compounds, the corundum structure is the most stable and does not display any imaginary frequencies. Calculations targeted at a high-pressure synthesis starting from the stable oxides and metals predict a reaction pressure of 15 GPa for Mo2O3 and over 60 GPa for W2O3
