  The concept of {\it equivalent systems} from the thermodynamic point of view,
originally introduced by Th. De Donder and I. Prigogine, is deeply investigated
and revised. From our point of view, two systems are thermodynamically
equivalent if, under transformation of the thermodynamic forces, both the
entropy production and the Glansdorff-Prigogine dissipative quantity remain
unaltered. This kind of transformations may be referred to as the {\it
Thermodynamic Coordinate Transformations} (TCT). The general class of
transformations satisfying the TCT is determined. We shall see that, also in
the nonlinear region ({\it i.e.}, out of the Onsager region), the TCT preserve
the reciprocity relations of the transformed transport matrix. The equivalent
character of two transformations under TCT, leads to the concept of {\it
Thermodynamic Covariance Principle} (TCP) stating that all thermodynamic
equations involving the thermodynamic forces and flows ({\it e.g.}, the closure
flux-force relations) should be covariant under TCT.
