Isoparaffin-olefin alkylation was investigated using liquid as well as solid onium poly(hydrogen fluoride) catalysts. These new immobilized anhydrous HF catalysts contain varied amines and nitrogen-containing polymers as complexing agents. The liquid poly(hydrogen fluoride) complexes of amines are typical ionic liquids, which are convenient media and serve as HF equivalent catalysts with decreased volatility for isoparaffin-olefin alkylation. Polymeric solid amine:poly(hydrogen fluoride) complexes are excellent solid HF equivalents for similar alkylation acid catalysis. Isobutane-isobutylene or 2-butene alkylation gave excellent yields of high octane alkylates (up to RON = 94). Apart from their excellent catalytic performance, the new catalyst systems significantly reduce environmental hazards due to the low volatility of complexed HF. They represent a new, "green" class of catalyst systems for alkylation reactions, maintaining activity of HF while minimizing its environmental hazards.