Abstract: Improved isoparaffin-olefin alkylation solid catalyst processes are provided which are characterized by low coke laydown and catalyst deactivation rates and production of valuable branched chain, high octane number alkylates. The processes of the invention involve providing a starting reactant mixture comprising an isoparaffin, an olefin and a co-solvent or diluent (carbon dioxide in molar excess, methane, hydrogen or mixtures thereof), and contacting the reactant mixture with an alkylation catalyst at near-critical or preferably supercritical conditions for the reaction mixture. The carbon dioxide serves as a co-solvent and reduces the critical temperature (T.sub.c) of the reaction mixture, thereby allowing lower reaction temperatures. The isoparaffin and olefin reactants are preferably pretreated to minimize moisture, peroxide and oxygenate impurities therein.