Dislocation loop nucleation is analyzed using a rate theory based model for face-centered cubic (fcc) binary alloys containing A- and B- atoms. The model considers three types of interstitial dumbbells composed of A- and B-atoms, AA-, BB-, and AB-type dumbbells. Based on the movements of these dumbbells to the nearest neighbor lattice sites, conversion processes between their different types are introduced in the formulation. A di-interstitial is assumed to be the nucleus of a dislocation loop, and reactions of point defect production by irradiation, mutual recombination of an interstitial and a vacancy, dislocation loop nucleation, and their growth are also included. Calculations are performed, varying the composition and binding strength between the two component atoms. Different types of kinetics are obtained in accordance with the dominant loop nucleus type. Conversion between interstitial dumbbells is demonstrated to play an important role in determining the concentration of interstitials, and consequently, to affect the kinetics of loop nucleation. The present model also predicts that the average composition of the formed loops differs from that of the matrix.