A kinetic Ising model is applied to the description of phase transformations on a Bethe lattice. A closed set of kinetic equations for a model with the coordination number q=3 is obtained using a procedure developed in a previous paper. For T close to T-c (T>T-c), where T-c is the phase transition temperature, and zero external field (absence of supersaturation), the rate of phase transformation (RPT) for small deviations from equilibrium is independent of time and tends to zero as (T-T-c). At T=T-c, the RPT depends on time and for large times behaves as t(-1). For T0. The role of different mechanisms responsible for growth (decay), splitting (coagulation), and creation (annihilation) of clusters are examined separately. In all cases there is a critical value B-c of the external field, such that the phase transformation takes place only for B-f>B-c. This result is also obtained from a more simple consideration involving spherical-like clusters on a Bethe lattice. The characteristic time t(R) at which the polarization becomes larger than zero diverges as (B-f-B-c)(-b) for B-f-->B-c with b=0.47. The RPT has a rapid growth near t(R) and remains constant for t>t(R). The average cluster size (number of spins in a cluster) exhibits a rapid unrestricted growth at a time t(d)similar or equal tot(R) which indicates the creation of infinite clusters. The only exception to the latter behavior occurs when the kinetics is dominated by cluster growth and decay processes. In this case, the average cluster size remains finite during the transformation process. In contrast to the classical theory, the present approach does not separate the processes of creation of clusters of critical size (nucleation) and of their growth, both being accounted for by the kinetic equations employed. (C) 2004 American Institute of Physics.