We discuss the principle of minimum entropy production as proposed by Prigogine, providing two examples (heat conduction in a fluid at rest and the combined shear flow and heat conduction in in incompressible fluid) for which the principle produces field equations that do not agree with the balance equations of continuum mechanics. We have not been able to find any special assumption on the temperature dependence oil the phenomenological coefficients (such its thermal conductivity and dynamical viscosity) under which a general agreement between standard balance equations and balance equations determined by the minimum entropy production principle call be stated. A critical analysis of the theorem proof shows that the minimum entropy production of system in a stationary state cannot be different from zero. (C) 2007 Elsevier Ltd. All rights reserved.