Let G be a complex semi-simple Lie group and form its maximal flag manifold F = GIP = U/T where P is a minimal parabolic (Borel) subgroup, U a compact real form and T = U boolean AND P a maximal torus of U. We study U-invariant almost Hermitian structures on F. The (1, 2)-symplectic (or quasi-Kahler) structures are naturally related to the affine Weyl groups. A special form for them, involving abelian ideals of a Borel subalgebra, is derived. From the (1, 2)-symplectic structures a classification of the whole set of invariant structures is provided showing, in particular, that nearly Kahler invariant structures are Kahler, except in the A(2) case. (C) 2003 Elsevier Inc. All rights reserved.1782277310