The activities of supported heteropolyacids H3PW12O40 and H3PTiW11O39 and sulfonated zirconium dioxide were studied and compared in isobutane alkylation with butenes. The conversion of the isobutane-butene feedstock in the presence of H3PW12O40 possessing, only strong Bronsted acidity was exclusively due to the oligomerization of butenes. The catalyst based on the titanium-containing heteropolyacid, which can exhibit electron-acceptor properties, was active in alkylation. Correlation between the activity in alkylation and the strength of Lewis acid sites was revealed for the supported zirconium sulfate catalysts. It was shown that zirconium hydrides are produced in the interaction of isobutane with the zirconium sulfate catalysts, which can be responsible for the appearance of the tert-butyl cation as the key alkylation intermediate. The mechanism of isobutane alkylation with butenes on solid acid catalysts is discussed.