A physically-based model is proposed for the competitive precipitation of multiple phases (bcc-Fe, Fe3B, Nd2Fe14B, Nd2Fe23B3, NdFe4B4 and Fe2B) from an amorphous Fe-B-Nd matrix. These materials form the basis of a class of nanocomposite hard magnets. The nucleation and growth of the different phases are calculated using computational thermodynamics and kinetics tools with input from a thermodynamic assessment of this system. In some alloy compositions, the phase formation sequence during crystallization shows significant sensitivity to the heating-rate. Model calculations illustrate that this effect cannot be explained by homogeneous nucleation and growth of the phases. The possible role of heterogeneous nucleation is briefly discussed.