The structures and intrinsic gas-phase acidities (GA) of some dodecaborane acids, the derivatives of YB12H11H (Y = PF3, NH3, NF3, NMe3), B12H12H2, and B12H12H- (HA, H(2)A, and HA-, respectively) have been computationally explored with DFT B3LYP method at the 6-311+G** level of theory as new possible directions of creating superstrong Bronsted acids. Depending on the nature and number of the substituents different protonation geometries were investigated. In general, the GA values of the neutral systems varied according to the substituents in the following order: CF3 < F < Cl and in case of anionic acids: CF3 < Cl < F. The dodecatrifluoromethyl derivative of H(2)A, B-12(CF3)(12)H1H2, emerges as the strongest among the considered acids and is expected to be in the gas phase at least as strong as the undecatrifluoromethyl carborane, CB11(CF3)(11)H1H. The GA values of the respective monoanionic forms of the considered acids all, but the (CF3)(11) derivative, remained higher than the widely used threshold of superacidity. The HA derivatives (Y = PF3, NF3) GAs were approximately in the same range as the H(2)A acids. In the case Y = NH3 or NMe3 the GA values were significantly higher. Also, the pK(a) values of B12H12H2, CB11H12H, and their perfluorinated derivatives in 1,2-dichloroethane (DCE) were estimated with SMD and cluster-continuum model calculations. The obtained estimates of pK(a) values of the perfluorinated derivatives are by around 30 units lower than that of trifluoromethylsulfonylimide, making these acids the strongest ever predicted in solution. The derivatives of B12H12H2 are as a rule not significantly weaker acids than the respective derivatives of CB11H12H. This is important for expanding practical applicability of this type of acids and their anions, as they are synthetically much more accessible than the corresponding CB11H12- derivatives.