Broad-band ULF fluctuations are routinely observed upstream of the terrestrial magnetosphere: their amplitude, fairly large in the whole magnetosheath, peaks at the magnetopause, and decays to very small values in the magnetosphere. We test the idea that the source of all these fluctuations is in the magnetosheath and that the high magnetopause level is an amplification effet due to propagation. Starting from given stable magnetosonic waves in the magnetosheath, their behaviour is calculated when, during their propagation, they encounter the magnetopause density gradient. For a certain category of indicend waves, a ''resonant amplification'', occurring inside the gradient layer, is found. ¿American Geophysical Union 1994