The method of lifetime measurement has been used to investigate the kinetics of spontaneous boiling-up of superheated argon-helium and argon-neon solutions. Experiments were made at a pressure of p = 1.5 MPa and concentrations up to 0.33 mol% in the range of nucleation rates from 101 to 101 s(-1) m(-3). The homogeneous nucleation regime has been distinguished. With good agreement between experimental data and homogeneous nucleation theory in temperature and concentration dependences of the nucleation rate, a systematic underestimation by 0.25-0.34 K has been revealed in superheat temperatures over the saturated line attained by experiment as compared with theoretical values calculated in a macroscopic approximation. The revealed disagreement between theory and experiment is connected with the dependence of the properties of new-phase nuclei on their size.