The synthesis, characterisation, and crystal structure determination of the closely related compounds 3,3'-bi-(5-trifluoromethyl-1,2,4-oxadiazole) and 5,5'-bi-(2-trifluoromethyl-1,3,4-oxadiazole) are reported. These two compounds are known for their bioactivity; however, in this study they serve as model compounds to evaluate the suitability of the heterocyclic oxadiazole ring system for energetic materials when the fluorine atoms in the exocyclic CF3 groups are substituted successively by nitro groups. Quantum chemical calculations for the bi-1,3,4-oxadiazole derivatives with difluoronitromethyl, fluorodinitromethyl, and trinitromethyl groups have been carried out and predict promising energetic performances for both explosive and propulsive applications.