Time dependent nucleation theory has been applied to calculate temperature vs incubation time curves of competing phases, the nucleation temperatures and the critical cooling rates required for the formation of primary phases in undercooled melts. The incubation time is controlled by melt undercooling and diffusitivity in the melt especially at large undercooling. Larger melt undercoolings are required for the suppression of intermetallic phases with increasing solute content. The predicted hierarchy of phase selection in Al-TM (TM = Cr, Ti) alloys is in agreement with experimental results. The calculated phase boundaries on nucleation maps of Al-TM alloys are in agreement with experimental results, especially when heterogeneous volume nucleation is considered. The fit to experiment of calculations where the diffusion coefficient in the melt is related to viscosity is improved by considering Tg = 0.25T0.