We report nucleation-rate measurements in metastable liquid argon-krypton solutions at pressures of 1.0 and 1.6 MPa over a wide temperature and concentration range; These measurements were performed with the use of a superheated liquid lifetime measurement method. The experimental results are compared with the homogeneous nucleation theory data both using a macroscopic (capillary) approach and taking into account the dependence of critical bubble surface tension on interface curvature. The size effect in nucleation is considered in the framework of the Van-der-Waals, Cahn-Hilliard method. The experimental data indicate that the homogeneous nucleation theory quantitatively describes the kinetics of a first order phase transition in binary solutions of simple liquids if the size effect is taken into account and nucleation rates are J greater than or similar to 10(6) m(-3) sec(-1). At J less than or similar to 106 m(-3) sec(-1) there is initiated nucleation. A diffusion spinodal of a solution is approximated. The attainable superheating temperature data are presented.