After the description of the general structure of non-equilibrium (irreversible) thermodynamics, the local (or differential) principles developed previously are outlined in all the representations. Hereafter the universal form of the integral principle of thermodynamics is given from which transport equations governing irreversible processes are derived within the framework of a general “Γ” formalism. The derivation of the transport equations is followed by the discussion of the partial and alternative forms of the integral principle previously developed by us and by others. We demonstrate that the “local potential method” can be founded also in an exact manner by means of the partial form of our integral principle. In the following, the types of tasks and theories of non-linear thermodynamics are classified, further on, the general proof of a supplementary theorem is given, which has already been confirmed for the case of heat conduction. This theorem allows extension of the validity of the universal form of the integral principle to certain types of non-linear problems. Finally the relation of our integral principle to VOJTA's functional variational principle is discussed and it is stated that the two different formulations are the alternative representations of a single general principle, for which the name: “governing principle of dissipative processes” would be most appropriate.