A composition defined: either as comprising at least one Broensted acid, designated HB, dissolved in a liquid medium with an ionic nature of general formula Q+A-, in which Q+ represents an organic cation and A- represents an anion that is different from B, or as resulting from dissolving at least one Broensted acid, designated HB, in a non-aqueous liquid medium with an ionic nature of general formula Q+A-, in which Q+ represents an organic cation and A- represents an anion that is identical to the anion B, can be used as a catalyst and solvent in acid catalysis processes, in particular in the alkylation of aromatic hydrocarbons, the oligomerization of olefins, the dimerization of isobutene, the alkylation of olefins by isoparaffins, the isomerization of n-paraffins into isoparaffins, the isomerization of n-olefins into iso-olefins, the isomerization of the double bond of an olefin and the purification of an olefin mixture that contains branched alpha olefins as impurities.