We consider single-phase and multiphase disequilibrium processes in presence of nonlinear heat and mass transfer as well as chemical or electrochemical reactions. An approach accepted distinguishes in each elementary process, diffusive or chemical, two competing (unidirectional) fluxes. They are equal in the state of thermodynamic equilibrium and their difference off equilibrium constitutes the observed resulting flux representing the rate of chemical reaction. We stress the role of nonlinear chemical (electrochemical) resistance and chemical (electrochemical) affinity. The nonequilibrium systems under investigation are described by equations of nonlinear kinetics of Marcelin-de Donder type containing exponential terms with respect to chemical potentials of Planck and temperature reciprocal, that simultaneously are analytical expressions characterizing the transport of the substance or energy by the energy barrier. We show how the kinetics of this sort follows from the law of mass action, what are its consequences closely and far from equilibrium, and also how a basic equation of chemical or electrochemical kinetics (Butler-Volmer) emerges. We also stress the significance of nonlinear chemical (electrochemical) resistance and of the chemical (electrochemical) affinity. Simultaneously we stress restrictiveness of the discrete energy barrier, which is not capable of avoiding mean quantities characteristic of the whole barrier and connected with finite affinities or driving forces. To describe the chemical transformation as a motion through the energy barrier treated as a continuum an effort is made to replace the logarithmic chemical resistance (a mean quantity associated with a finite affinity) by its local counterpart. The result is a continuous description, governed by a principle of Fermat type with an infinite number of infinitesimal refractions of the ray. The results show that the path of chemical complex bends into a direction that ensures its shape associated with longest residence time in regions of lower resistivity. These properties make it possible to predict shapes of chemical paths. (C) 2003 Elsevier Ltd. All rights reserved.