Local equilibrium effect in systems with transport of energy, matter and electric charge is shown to be sufficient for local stability of the processes which satisfy a dissipative variational formalism for perturbations relaxing to a steady slate. It is postulated that the effect is an extremal property of those thermodynamic systems which minimize dissipation and whose evolution is governed by an extremum principle describing their natural tendency to Fast local relaxations. A pertinent principle extends that of Onsager’s [1] to nonstationary quasilinear regime and electrochemical transport. Its resulting form describes an extremum of a functional structure related to grand thermodynamic potential, the Legendere transform of entropy. The principle is set in the physical space-time rather than in the three-dimensional (3D) space and, as such, it substantiates the joint role of thermodynamic potentials and intensity of dissipation. For isolated systems the principle implies a least possible growth of entropy under constraints imposed by conservation laws, whereas for nonequilibrium steady-states its perturbational form implies minimum of a work potential at the steady slate. Phenomenological equations, equations of change and bulk overvoltage properties can be derived in complex electrochemical systems. Nonequilibrium temperatures and chemical potentials are interpreted in terms of the Lagrangian multipliers of conservation constraints. These quantities converge to the classical thermodynamic intensities when the local equilibrium is attained.