A generalized principle of designing superstrong Bronsted acids is suggested according to the following scheme: M=O --> M=Z(X)(n). It consists of the formal replacement of =O fragment in carbonyl, sulfonyl, etc. groups in various acidic systems (e.g., CH3CHO, FSO3H, where M is the CH3CH= or FSO2H=fragment, respectively) by =NSO2F, =NCN, =C(CN)(2), =P(SO2F)(3), =S(CN)(4), or any other formally bivalent group =Z(X)(n) (where the formal valency of the central atom Z is n + 2), leading to highly acidic systems (e.g., HC(=P(CN)(3))NH2, FS(=C(CN)(2))(2)OH, etc.). It is demonstrated that in several cases the introduction of the double-bonded substituent at the central atom (e.g., N, C, P, S, Cl) that carries the potentially acidic proton or the acidity site (e.g., OH, NH2, CH3, etc. groups) will lead to the enormous (up to ca. 120 kcal/mol or 88 pK(a), units!) increase of the intrinsic acidity of the respective parent acid. The acidity of the resulting acids and the scope and limitations of the principle are explored using density functional theory calculations at B3LYP 6-311 +G** level. Some of the resulting acids (or their anions) were found to undergo fragmentation in the course of the geometry optimization. The general trend that follows from the results of the calculations is that the stability of the resulting compounds is influenced by both the M and the Z. If M is a first row element (carbon or nitrogen), then stable species are produced with almost any Z, If M is a second row element (sulfur or phosphorus), then the species with first row Z are mostly predicted to be stable, but most of the species with second row Z are expected to undergo fragmentation during the geometry optimization. The Z = N and Z = C derivatives (e.g., =NSO2CF3, C(CN)(2), -C(So(2)CF(3))(2), etc,) are predicted to be the most stable. However, they have relatively modest electron-accepting power as compared to their penta-, hexa-, and heptavalent counterparts. The acidifying effects of the -Z(X)(n) groups with the same X increase with increasing n: NCN < =C(CN)(2) < =P(CN)(3) < =S(CN)(4) and =NSO2F < =C(SO2F)(2) < =P(SO2F)(3). Also, the acidifying effect of a fluorosulfonyl-substituted substituent is higher than that of the corresponding cyano-substituted substituent.