The processes of magnetization of ferrimagnetic Heisenberg chains of alternating spins are studied theoretically. Size-scaling analysis with the exact diagonalization of finite systems for (S,s) = (3/2,1) and (2,1) indicates a multi-plateau structure in the ground-state magnetization curve for S and s>1/2. The first plateau in the spontaneous magnetization can be explained classically: as originating from the Ising gap. In contrast, the second and higher ones must be originating from the quantization of the magnetization. It is also found that all of the 2s plateaux, both classical and quantum ones, appear even in the isotropic case with no bond alternation.