This paper reports on some propagation effects occurring while the ionosphere consists of several layers. A few simple model problems are considered to show in which way this multi-layer structure can yield a new set of ELF resonance phenomena. The resonances appear in the space between the Earth and layer interfaces or inside the layers and are liable to give rise to peaks or minima in the frequency dependencies of ELF electromagnetic fields both for the cosmic and terrestrial sources. Calculations have been made for the real ionospheric models and distant Earth's sources have shown that such a mechanism can explain some experimental data including the effect of ''Evening Ionosphere Radiation'' by Schecotov and Molchanov (1985). ¿ American Geophysical Union 1994