NOVELTY - The fuel cells useful as a power source for portable/mobile appliances, comprises an electrolyte membrane, a pair of electrodes disposed on both sides of the electrolyte membrane, a catalyst supported on a carbon nanotube, and an electrolyte resin coating the carbon nanotube. The electrodes has the carbon nanotube, which is oriented with an inclination greater than or equal to 10degrees or less than or equal to 30degrees with respect to a planar direction of the electrolyte membrane. An end of the carbon nanotube is embedded in the electrolyte membrane. The carbon nanotube has an outer surface and an amorphous layer.    USE - Useful as a power source for portable or mobile appliances.    ADVANTAGE - The fuel cells improve a power generation efficiency, are free from the restrictions of a carnot cycle and exhibit high energy conversion efficiency.    DETAILED DESCRIPTION - The fuel cells useful as a power source for portable/mobile appliances, comprises an electrolyte membrane, a pair of electrodes disposed on both sides of the electrolyte membrane, a catalyst supported on a carbon nanotube, and an electrolyte resin coating the carbon nanotube. The electrodes has the carbon nanotube, which is oriented with an inclination greater than or equal to 10degrees or less than or equal to 30degrees with respect to a planar direction of the electrolyte membrane. An end of the carbon nanotube is embedded in the electrolyte membrane. The carbon nanotube has an outer surface and an amorphous layer. A thickness of the amorphous layer is greater than or equal to 1 nm and less than or equal to 3 nm. The carbon nanotube is an electrically conductive material whose column diameter is greater than or equal to 5 nm and less than or equal to 50 nm, length is greater than or equal to 10 microns and less than or equal to 80 microns, and aspect ratio is greater than or equal to 500 and less than or equal to 10,000. The electrolyte resin is a perfluorocarbon sulfonic acid resin, and a hydrocarbon polymer, which has a proton conductive group in a side chain. An INDEPENDENT CLAIM is included for a production method for a fuel cell.    DESCRIPTION OF DRAWING(S) - The diagram shows the fuel cell:    Electrolyte membrane; (1)    Electrically conductive nanocolumn; (4)    Catalyst; (5)    Electrolyte resin. (6)