The kinetics of isothermal crystallization of the droplets in polydisperse emulsions are analyzed under the condition that each emulsion droplet gives birth to one nucleus only. Expressions are derived for the time dependences of the number of crystallized droplets and the fraction of crystallized droplet volume in the cases of either volume or surface nucleation of the crystals in the droplets. The time for half-crystallization is determined as a function of the emulsion polydispersity, and it is found that the more polydisperse the emulsion, the shorter this time in comparison with that for the corresponding monodisperse emulsion. Formulae are also obtained for the change of the velocity upsilon of propagation of ultrasound through polydisperse emulsions during the time t of isothermal crystallization of the droplets in them. Good agreement is found between theory and experiment in an analysis of available upsilon(t) data for crystallization in polydisperse palm oil-in-water and n-hexadecane-in-water emulsions. The results obtained are directly applicable to devitrification and polymorphic transformation of disperse solid phases.