  Using special quasigraded Lie algebras we obtain new hierarchies of
integrable nonlinear vector equations admitting zero-curvature representations.
Among them the most interesting is extension of the generalized Landau-Lifshitz
hierarchy which we call "doubled" generalized Landau-Lifshiz hierarchy. This
hierarchy can be also interpreted as an anisotropic vector generalization of
"modified" Sine-Gordon hierarchy or as a very special vector generalization of
so(3) anisotropic chiral field hierarchy.
