  The behavior of Haldane-gap antiferromagnets in strong magnetic field is not
universal. While the low-energy physics of the conventional 1D spin-1
Heisenberg model in its magnetized regime is described by one incommensurate
soft mode, other systems with somewhat perturbed coupling constants can possess
two characteristic soft modes in a certain range of the field strength. Such a
{\em two}-component Lutinger liquid phase is realised above the massive
Haldane-gap phase, and in general above any massive nonmagnetic phase, when the
ground state exhibits short range incommensurate fluctuations already in the
absence of the field.
