In the theoretical description of nucleation-growth processes, currently Gibbs's classical thermodynamic theory of heterogeneous systems is predominantly employed for the description of the properties of the clusters. However, Gibbs's approach does not make it possible to describe, in general, the properties of critical clusters (determining the rate of nucleation) in a sufficiently correct way. Moreover, Gibbs's approach is restricted by its applicability to thermodynamic equilibrium states exclusively. For this reason, it does not give a theoretically founded prescription for a determination of the possible states of clusters of sub- and supercritical sizes in dependence on supersaturation and size of the clusters. In order to overcome these shortcomings, in recent years a generalization of Gibbs's classical approach has been developed and employed for the description of nucleation processes. This generalization of Gibbs' classical method leads, for a variety of different applications, to dependencies of the work of critical cluster formation on supersaturation, which are qualitatively and widely even quantitatively in agreement with density-functional computations. The theoretical methods and results are summarized in the first part of the present paper. They are then extended for the first time to a description of processes of growth of single clusters and ensembles of clusters. In order to fulfill this task, a new method for determination of the parameters of sub- and supercritical clusters is developed. It turns out as the result of the analysis that a variety of thermodynamic and kinetic parameters, determining cluster growth, become dependent on cluster size as well. The results are illustrated for a model system (segregation in regular solutions) and applied to the interpretation of experimental results on segregation processes in solutions and crystallization processes in glass-forming melts. It is shown that the newly developed approach resolves a variety of problems in the interpretation of experimental data on the kinetics of phase formation processes which could not be given a satisfactory explanation so far. (C) 2003 Elsevier Inc. All rights reserved.