Abstract Although many papers concerning the continuum theory of mixtures have been produced in the last years, the adequate form for the first and second laws of thermodynamics is still a controversial subject. In this paper, the basic principles that govern the evolution of a continuous mixture are postulated and used to develop a systematic procedure to obtain thermodynamically admissible objective constitutive equations. The prescription of five thermodynamic potentials is sufficient to define a complete set of constitutive relations. Two examples concerning the thermal analysis of a binary mixture of rigid solids and fluid flow in a porous channel bounded by two isothermal impermeable plates are presented. They illustrate the possibilities of effective practical use of the proposed theory.