A multi-layer coating for protection of metals and alloys against oxidation at high temperatures is provided. The invention utilizes a multi-layer ceramic coating on metals or alloys for increased oxidation-resistance, comprising at least two layers, wherein the first layer (3) and the second layer (4) both comprise an oxide, and wherein the first layer (3) has a tracer diffusion coefficient for cations Mm+, where M is the scale forming element of the alloy, and the second layer (4) has a tracer diffusion coefficient for oxygen ions O2− satisfying the following formula: ∫ ln ⁢ ⁢ p ⁡ ( O 2 ) in ln ⁢ ⁢ p ⁡ ( O 2 ) ex ⁢ ( D O + m 2 ⁢ D M ) ⁢ ⁢ ⅆ ln ⁢ ⁢ p ⁡ ( O 2 )