Production of minute sintered coat on a porous substrate consists of a slurry coat process of coarse powder low differential pressure, using plus pressure and 0 differential pressure on the coat-formed surface side, of application of comparatively low differential pressure between the coat-formed surface of a porous substrate and the surface of its opposite side (opposite coat-formed surface). The slurry (coarse powder slurry) containing the film substance of comparatively large particle size is applied, and then, dried later. Fine powder of high differential pressure between the above both surfaces is used. The slurry (fine powder slurry) containing the film substance of comparatively small particle size is applied, and then, dried later. The slurry films formed by coating in both these processes are co-burnt, and at first, the above coarse powder low differential pressure slurry coat process is performed, and then, the fine powder high differential pressure slurry coat process is performed and after that, both processes are performed sequentially.    Also claimed is a method for forming minute sintered coat on the exterior (film-formed surface) of a cylindrical porous substrate consisting of a slurry coat process of coarse powder low differential pressure, a slurry coat process of fine powder high differential pressure and a burning process.    ADVANTAGE -   Even though the number of burning times is little, thin minute ceramic thin films can be obtained by using this method. Therefore, the performance of ceramics heaters, fuel cells and the other elements can be improved, and also the production costs can be lowered. Since burning failure of the coat can be controlled. Yield of the production of the coat can be improved. Ceramic thin films can be formed all over the surfaces of substrates of various shapes (flat substrate, the insides or outsides of pipes) or arbitrary parts of them. In comparison with CVD process (chemical vapour deposition process) and plasma spraying coating process, expensive production equipment is not necessary and this method can be easily applied to commodities of large dimension.