Herein we report the covalent functionalization of multiwall carbon nanotubes by grafting sulfanilic acid and their dispersion into sulfonated poly(ether ether ketone). The nanocomposites were explored as an option for tuning the proton and electron conductivity, swelling, water and alcohol permeability aiming at nanostructured membranes and electrodes for application in alcohol or hydrogen fuel cells and other electrochemical devices. The nanocomposites were extensively characterized, by studying their physicochemical and electrochemical properties. They were processed as self-supporting films with high mechanical stability, proton conductivity of 4.47×10−2 Scm−1 at 30°C and 16.8×10−2 Scm−1 at 80°C and 100% humidity level, electron conductivity much higher than for the plain polymer. The methanol permeability could be reduced to 1/20, keeping water permeability at reasonable values. The ratio of bound water also increases with increasing content of sulfonated filler, helping in keeping water in the polymer in conditions of low external humidity level.