A simple lattice-gas model is studied (Sec. II) which serves to illustrate the following points. If a system approaches equilibrium with its surroundings through only such processes as involve exchange between system and surroundings (i.e., no internal processes are available to the system) and if the kinetic behavior of the system depends on internal parameters as well as on thermodynamic variables, then in general the system will not achieve internal equilibrium prior to the final state of equilibrium with the surroundings. The usual flux-force equations and reciprocal relations of irreversible thermodynamics for such a system are concerned explicitly with thermodynamic variables and assume internal equilibrium with respect to the internal parameters. Therefore, in general, systems of the type referred to will not obey conventional flux-force equations nor exhibit reciprocal relations. The same conclusions would be expected if internal processes exist but are no faster than the exchange processes.