We report measurements of the conductivity of a series of mixtures of ionic liquids and acids. We find in particular that mixtures of 1-ethyl-3-methylimidazolium (EMI, C6H11N2)-bis(trifluoromethylsulfonyl)imide [TFSI, (CF3SO2)(2)N] with the acid H-TFSI have promising conduction properties for applications to fuel cell membranes. However, these mixtures have a peculiar dependence of conductivity on acid concentration. We present a series of model calculations at coarse-grained and molecular dynamics levels which suggest that the observed nonmonotonic dependence of conductivity on acid concentration arises because of proton clustering in the mixtures and possibly because of phase separation at the higher acid concentrations.