<p><b>Abstract</b>—A mathematical model is formulated for the bulk crystallization of supercooled binary melts with allowance for a nonlinear growth rate of nuclei and fluctuations in their growth rates. The model consists of a second-order kinetic equation for the crystal size distribution function, integral heat-and-mass balance equations, and boundary and initial conditions. Various growth laws are considered for spherical particles in single- and two-stage nucleation, and they are introduced into kinetic and balance equations. A complete analytical solution to the formulated integro-differential model is found in a parametric form: the dynamics of melt supercooling, the melt temperature, the impurity concentration, the crystal size distribution function, and its moments are determined. The solution parameter is modified time, which is related to ordinary time through an integral relation dependent on an individual crystal growth rate law. The analytical solution also depends on the nucleation frequency, which is influenced by the supercooling of a binary melt and its concentration. The Weber–Volmer–Frenkel–Zeldovich (WVFZ) and Meirs nucleation frequencies are considered. The obtained analytical solution is illustrated for a Ti–Al melt: parametric solutions (dependent on modified time) and solutions dependent on dimensionless time are shown. The supercooling of a binary melt is shown to decrease in time due to the release of latent heat of the phase transformation by growing crystals. The crystal size distribution function is bell-shaped and diffuses in particle size space toward large radii. The maximum of the distribution function decreases over time, and its bell-shaped form becomes wider. The developed theory is compared with various experimental data.</p>