International audienceA thermodynamic derivation is given for the representation of a system having viscoelastic or relaxationproperties by means of a potential and dissipation function familiar in Lagrangian mechanics. This leads to modes of relaxation which are used as normal coordinates to derive general expressions for operational tensors relating stress and strain. A large variety of phenomena involving interaction of diffusion,chemical reaction, heat transfer, mechanical deformation, etc., is included in this theory