Electromagnetic levitation technique is applied to undercool bulk melts of metals and alloys. A large undercooling range becomes accessible by avoiding heterogeneous nucleation on container walls and processing the melts under high purity environment. A freely suspended drop is produced with the extra benefit that it becomes accessible for direct observation and diagnostics. Temperature-time profiles (ttp) are measured during the melting and solidification process. The up profiles give insight into the thermodynamics of phase-selection processes. The levitation technique is combined with the diagnostic means at European Synchrotron Radiation Facility (ESRF Grenoble) to record time-resolved diffraction spectra during rapid crystallization of deeply undercooled melts. In such a way, the sequence of solidification of different crystallographic phases and (partly) remelting of primarily formed phases during recalescence is unambiguously determined. All these investigations allow for the construction of nucleation phase-selection diagrams examples of which are presented for Fe-based, Ni-V, and Nd-Fe-B alloys with a competition of phase formation of bcc, fee, and some intermetallic phases, respectively. They give the conditions for the formation of metastable solids of different crystallographic structures as a function of concentration and undercooling achieved prior to solidification. (C) 2003 Elsevier B.V. All rights reserved.