Aerogels based on polytetrafluoroethylene (60 and 50 mass %) and graphene oxide were obtained. After hydrazine reduction and annealing in an inert atmosphere, the aerogels became superhydrophobic with a contact wetting angle on the outer surface of 166-170 degrees. The pore size distribution was measured by the method of standard contact porosimetry in the range of 1 divided by 10(5) nm with octane and water as working fluids. It was found that the wettability of the small pores with water was higher than that with octane. Internal hydrophilicity was due to the "swelling" of the hydrated -CO and -COH groups, the presence of which was confirmed by IR spectroscopy and X-ray photoelectron (XPS) spectroscopy. Thus, the aerogels had a superhydrophobic outer surface and a superhydrophilic inner surface. The presence of the hydrophilic pores in aerogels also explained the shape of the cyclic volt-farad curves in a 1 M H2SO4 solution. Further, electroreduction of molecular oxygen at platinum deposited on aerogels was studied, and it was shown that the limiting diffusion currents of oxygen reduction at aerogel-supported platinum could be higher than those at a standard Pt (20%)/Vulcan XC-72 catalyst due to the superhydrophobic surface properties of the aerogels.