The amplitude dependence of the relative AC losses q in anisotropic superco
nducting plate-like samples has been studied experimentally and theoretical
ly. Contrary to the isotropic case where there exists one maximum in the de
pendence of q = chi" on me amplitude h(0) of the AC magnetic field, two max
ima in the dependence q(h(0)) were observed. Both maxima are found to be re
lated to the penetration of the AC field up to the middle of a sample. This
size effect occurs if the direction of the AC magnetic field differs signi
ficantly from the principal axes of symmetry. Such an unusual manifestation
of the size effect can be understood under the assumption that two compone
nts of the AC field along the principal axes of symmetry are independently
shielded by the two principal components of the anisotropic critical curren
t density. The obtained results are interpreted within the framework of the
critical state model generalized to the anisotropic case. (C) 2001 Elsevie
r Science B.V. All rights reserved.