"Conjunct oligomerization" of propylene or the isopentane-propylene alkylation catalyzed by an excess of 95% sulfuric acid was performed in two consecutive steps. First di-isopropylsulfate was prepared by interaction of sulfuric acid with propylene. The ester was then either decomposed at room temperature in the presence of the 5-10 molar excess of 95% acid or was used in the acid-catalyzed alkylation of isopentane. In situ H-1 and C-13 NMR study of the reaction mixture of "conjunct oligomerization" indicated that the diester participates in two equilibria with sulfuric acid. The first one transforms the diester into a monoester. The second equilibrium corresponds to protonation of the monoester with an excess of sulfuric acid. This converts a minor fraction of the mono-alkylsulfate into isopropyl carbenium ions that are only weakly solvated with sulfuric acid: C3H7HSO4 + H2SO4 reversible arrow C3H7+ H2SO4 + HSO4-. The subsequent reactions of alkyl carbenium ions with the non-protonated alkylsulfate result in final products of "conjunct oligomerization" while in the presence in the reaction mixture of isopentane, alkylation with the predominant formation of C-8 branched paraffins takes place. A very low yield of propane indicates a minor role of hydride transfer in alkylation. Another unexpected result is the absence in both reaction mixtures of propylene. These findings are in contradiction with the classical mechanism of isoparaffin-olefin alkylation by Schmerling. Therefore, an alternative mechanism of this reaction is suggested via a direct alkylation of isopentane with the mono-alkylsulfate.