We discuss the critical behaviour of the spin-(1,½) Heisenberg ferrimagnetic chain in a magnetic field, whose magnetization curve exhibits a plateau at a third of the full magnetization. A bond alternation stabilizes the massive state, whereas an exchange anisotropy causes the breakdown of the plateau and the onset of a gapless spin-fluid state, where the transition, lying in the XY but ferromagnetic region, is of Kosterlitz-Thouless type. In order to elucidate significant quantum effects, we investigate the model of the classical version as well.