In this paper, the conditions required separately for the infrared stealth and radar stealth are analyzed in view of the materials. The critical technology of infrared and radar compound stealth is indicated. That is, when using multilayer paint, the radar wave should be allowed to penetrate smoothly into the radar stealth layer while the low emissivity requirement of the infrared stealth layer is satisfied. Finally, the possibility for using doped semiconductor and nanometer material to achieve infrared and radar compound stealth is presented.