An approach is developed that enables one for nonlinear systems which, in particular, include systems with phase transformations due to homogeneous nucleation, to recover near equilibrium linear relations between the fluxes and thermodynamic forces for the thermodynamics of irreversible processes. In the case of crystal growth through the formation of two-dimensional nucleating centers the proposed description leads to a linear dependence of the growth rate on the difference between the chemical potentials of the bulk phases.