The present paper is concerned with the formulation of the generalization of theories describing heat and mass flows in a continuous medium. The considerations are based on the non-equilibrium thermodynamics. As a result the fundamental equations for the mass and heat fluxes and for the thermodynamic and mechanical fields, are obtained and the corresponding set of differential equations is formulated. Certain differences are pointed out between the general theories presented here and the thermodiffusion theory and the theory of mixtures. A thermodynamic variational principle is constructed. All the investigations concern only flows with a single temperature held.