Analysis of diffusion phenomena in a multilayer system, which we often encounter in electrochemical systems, comprises certain difficulties. To overcome them, we have developed an algorithm using numerical inversion of the Laplace transform of the diffusion equation. This procedure was applied to experiments involving hydrogen permeation in an electrochemical testing cell. Hydrogen permeation through a composite layer of nickel coated iron was measured. The coating was performed at one side or both sides of the specimen: two- and three-layers, respectively. In the two-layer system, the single layer approximation did not work when the thickness ratio between the coating and the substrate exceeded ca. 2x10(-4). On the other hand, the multilayer analysis well reproduced the experimentally obtained permeation current vs. time curve; further, the diffusion coefficient of the coating layer was in agreement with the value of nickel. However, there were some difficulties in the analysis for the three-layer system.