TECHNOLOGY FOCUS - INORGANIC CHEMISTRY - Preferred Method: In supplying the first supercritical fluid, the first supercritical fluid controlled to be the first temperature is circulated between a first heat exchanger that controls the temperature of the first supercritical fluid at the first temperature and the support. The precursor is added to the first supercritical fluid in an amount equivalent to an amount of the precursor consumed to cause the metal or the alloy to be supported on the support. The first supercritical fluid controlled to be the first temperature is supplied to the support to cause the precursor to be adsorbed on the support; and then the precursor is thermally decomposed at a third temperature to cause the metal or the alloy to be precipitated on the support. The second temperature of the support is higher than the first temperature of the first supercritical fluid, and less than the third temperature at which the precursor is thermally decomposed. A difference between the first temperature of the first supercritical fluid and the second temperature of the support is set at 5-100 degrees C. The third temperature of the support is higher than the second temperature of the support. A difference between the second temperature of the support and the third temperature of the support is set at 20-500 degrees C. The third temperature of the support is equal to or higher than a temperature at which the precursor is thermally decomposed. In method (M1), a temperature of the second supercritical fluid containing an ionomer dissolved in it is independently controlled to be a fourth temperature; the temperature of the support is independently controlled to be a fifth temperature higher than the fourth temperature of the second supercritical fluid; and the second supercritical fluid controlled to be the fourth temperature is supplied to the support and the metal or the alloy supported on the support, to coat the support and the metal or the alloy supported on the support with the ionomer. A second heat exchanger for controlling the temperature of the second supercritical fluid to be the fourth temperature is disposed, and the second supercritical fluid controlled to be the fourth temperature is circulated between the second heat exchanger and the support to cause supply the second supercritical fluid to the support. The ionomer is added to the second supercritical fluid in an amount equivalent to an amount of the ionomer consumed by coating the support, and the metal or the alloy supported on the support with the ionomer. A difference between the fourth temperature of the second supercritical fluid and the fifth temperature of the support is set at 5-100 degrees C. Preferred Components: The precursor is a precursor of one metal or a precursor of an alloy including at least two metals selected from platinum, cobalt, palladium, copper, titanium, gold, silver, ruthenium, chromium, iron, manganese, nickel, rhodium, iridium, and tin. The support is at least one support selected from carbon nanotube, carbon powder, titanium, silicon, tin, copper, titania, silica, and tin oxide.    TECHNOLOGY FOCUS - INSTRUMENTATION AND TESTING - Preferred Apparatus: The apparatus further comprises: an addition unit for adding the precursor to the first supercritical fluid in an amount equivalent to an amount of the precursor consumed, to cause the metal or the alloy to be supported on the support. The apparatus further comprises: a third temperature control unit for independently controlling a temperature of a second supercritical fluid containing an ionomer dissolved in it to be a fourth temperature; a fourth temperature control unit for independently controlling the temperature of the support to be a fifth temperature higher than the fourth temperature of the second supercritical fluid; and a second transfer unit for supplying the second supercritical fluid controlled to be the fourth temperature to the support and the metal or the alloy supported on the support. The apparatus further comprises: an addition unit for adding the ionomer to the second supercritical fluid in an amount equivalent to an amount of the ionomer consumed by coating the support, and the metal or the alloy supported on the support with the ionomer. Preferred Components: The first heat exchanger is disposed as the first temperature control unit, and the first supercritical fluid is circulated between the first heat exchanger and the support to supply the first supercritical fluid to the support. A second heat exchanger is disposed as the third temperature control unit, and the second supercritical fluid is circulated between the second heat exchanger and the support.    TECHNOLOGY FOCUS - ORGANIC CHEMISTRY - Preferred Components: The first supercritical fluid is at least one supercritical fluid selected from carbon dioxide, and trifluoromethane (CHF3). The second supercritical fluid is at least one supercritical fluid selected from trifluoromethane (CHF3), tetrafluoroethylene (CF2=CF2), 1,1,2,2-tetrafluoroethane (CHF2CHF2), pentafluoroethane (CF3CHF2), water, ethanol, and methanol (preferably CHF3, CF2=CF2, CHF2CHF2 or CF3CHF2).    TECHNOLOGY FOCUS - POLYMERS - Preferred Components: The ionomer is at least one ionomer selected from perfluorocarbon sulfonate resins, aromatic polyether sulfonate resins, aromatic polyimide sulfonate resins, and polybenzsulfonate resins. EXAMPLE - No suitable example given.