A membrane electrode assembly and fuel cell having such assembly. The membrane electrode assembly has a polymer electrolyte membrane, two catalytic electrodes in contact with the polymer electrolyte membrane on both sides, namely an anode and a cathode, and two gas diffusion layers directly or indirectly adjoining the electrodes, namely an anode-side gas diffusion layer and a cathode-side gas diffusion layer. At least one of the gas diffusion layers may optionally feature a microporous layer facing the polymer electrolyte membrane. The sequence of layers is anode-side gas diffusion layer, anode-side microporous layer, anode, polymer electrolyte membrane, cathode, cathode-side microporous layer, cathode-side gas diffusion layer. A relative hydrophobicity of at least two of these components and/or a hydrophobicity gradient within at least one of these components, and a relative pore structure having pore size and/or porosity of at least two of these components and/or a gradient within the pore structure of at least one of these components, is designed in such a way that it promotes the transport of water via the polymer electrolyte membrane, preferably from the cathode side to the anode side.