Improvement of the chemical stability of hybrid membranes based on perfluorosulfonic acid polymers is necessary to increase the lifetime of fuel cells. This article presents the results of the study of the transport properties and chemical stability of the hybrid Nafion® 212 membranes modified with nanoparticles of hydrated oxides SiO2, ZrO2, and TiO2 by in situ procedure. The influence of the nature of the dopant on the properties of the obtained materials is shown. The chemical degradation of the initial and hybrid membranes has been studied ex situ by treatment with Fenton’s reagent for 240 hours. The stability of materials increases in the series Nafion + SiO2 < Nafion + ZrO2 < Nafion < Nafion + TiO2. For the Nafion + TiO2 membrane the change in mass as a result of treatment with Fenton’s reagent is two times lower than for the initial Nafion membrane. This reveals an increase in the chemical stability of materials upon the incorporation of TiO2 nanoparticles due to their ability to bind free radicals. The maximum power of membrane-electrode assembly based on hybrid membranes containing TiO2 and SiO2 is higher than that based on Nafion® 212 by 7–10% at RH ~ 100% and t = 65°C.