Directional solidification studies have been conducted using Pb-Bi peritectic alloys over a wide range of compositions, temperature gradients, and growth velocities to characterize the primary α- to primary β-phase transitions, which have been observed at both very low and very high velocities. The critical conditions for these transitions correspond to the simultaneous growth of the α and β phases at or close to a single isotherm. The low velocity transition occurs under very specific conditions of composition, temperature gradient, and growth velocity. Since the transition conditions are composition dependent, they change continuously under terrestrial conditions where rejected solute is convectively mixed into the liquid. Detailed experimental studies have been carried out to examine the phase selection in the immediate vicinity of the critical velocity for the α to β transition, and the effect of convection on this transition is examined experimentally in the Pb-Bi system. The dynamic condition, at which both phases are present at the same isotherm, was shown to depend not only on velocities, temperature gradients, and bulk (nominal) alloy compositions, but also on the volume fractions of solid. A quantitative expression for the α- to β-phase transition condition was obtained by using the boundary layer model of fluid flow, which showed good agreement with the experimental results. It is shown that the transition occurs at the volume fraction where the bulk composition reaches the critical composition value predicted by the diffusive model. The modification in the microstructure map for the trailing planar or nonplanar β phase is discussed.