The properties of a resonance mode, the existence of which is related to the random local anisotropy K-l, detected in amorphous FeCoZr thin films, are reported. The data are compared with those obtained on a-CoZr(R) R = rare earth films where the amount of K-l was an order of magnitude bigger. The overall trends, evolution of the nature of the mode from a longitudinal via a mixed to a pure transverse state are the same. The parameters of the mode are directly related to the value of K-l. (C) 1999 American Institute of Physics. [S0021-8979(99)54808-1].