  We calculate magnetic anisotropy energy of Fe and Ni by taking into account
the effects of strong electronic correlations, spin-orbit coupling, and
non-collinearity of intra--atomic magnetization. The LDA+U method is used and
its equivalence to dynamical mean--field theory in the static limit is
emphasized. Both experimental magnitude of MAE and direction of magnetization
are predicted correctly near U=1.9 eV, J=1.2 eV for Ni and U=1.2 eV, J=0.8 eV
for Fe. Correlations modify the one--electron spectra which are now in better
agreement with experiments.
