Nucleation in binary alloys is studied in the capillary approximation of classical theory. By allowing both the size of the cluster and its composition to vary, the phase transition is investigated in a two-dimensional space. This parametrisation allows to derive diffusivities of the Fokker-Planck equation for the distribution function of clusters from the Cahn–Hilliard equation. It is shown how kinetics, together with thermodynamics, determine the direction of the nucleation current as well as the magnitude of the nucleation rate. The properties of the critical clusters and the direction of the nucleation current at the saddle point are derived for a generic model, from the binodal line to the spinodal limit. The critical clusters are found to exhibit properties that are very similar to that of non-classical theories. Once moderate supersaturation is reached, the interplay between kinetics and thermodynamics is found to invalidate the classical picture by modifying the direction of the nucleation current. The consequences on the magnitude of the rate of nucleation are discussed. The model is then applied to decomposition of FeCr solid solutions and is shown to constitute a reasonable sharp-interface approximation of the diffuse-interface theory of nucleation for the determination of both the cluster properties and the nucleation rate.