The experimental dissociation constants of strong acids are notoriously ill-defined, and it is necessary to rely on theoretical methods for their evaluation. We present a methodology for the theoretical evaluation of the dissociation constants, and the values of K-a for perchloric and sulfuric acids have been estimated. It has been shown that the acid dissociation constant K-a can be expressed as a product of two terms, K-a = K-a' X f(HA)(infinity), where K-a' is the apparent dissociation constant and f(HA)(infinity) is the infinite dilution activity coefficient of undissociated molecule of acid in liquid solution. The values of K-a' can be computed from readily available reference data. The limiting activity coefficients f(HA)(infinity) for strong acids can be determined by theoretical methods only. The following estimate for the limiting activity coefficients of perchloric and sulfuric acids has been obtained, -2.5 < log(10)f(HA)(infinity) < -1.3. The ranges of values of the dissociation constants of HClO4 and H2SO4 at 25 degrees C have been determined; log(10) K-a(HClO4) = 10.8-12.3; log(10) K-al(H2SO4) = 4.5-8.6.