Abstract: Objective of the present research is the proof of the Differential (generalized) Reciprocal Relations (DRR) between streams J_i and their moving forces X_j, more general, than Onsager-Cazimir’s relations and applicable not only to relaxing systems but also to the systems making useful work independence whether they are linear or not. Object of research is most the general class of spatially non-uniform systems not submitting to hypothesis of local equilibrium and to principle of linearity and supposing simultaneous flowing in them of a thermo-mechanical, thermo-electric, thermo-chemical, electro-magnetic, thermo-galvano-magnetic, etc., processes of transfer and transformation of energy. Primary results of research is essential expansion of area of applicability of Onsager-Cazimir’s reciprocal relations by their reception as consequences DRR, backgrounds of their fairness at inconstancy of basic kinetic coefficients L_ii and demonstrations of their applicability to processes of useful transformation of energy. In study is new more brief way of proof DRR and their universality; a conclusion to their basis of Maxwell’s equations; application DRR to a finding of the diagonal form of transport laws by simplification of a method of a finding of superposition effects without use of kinetic coefficients L_ij in them with its propagation on non-stationary processes. The practical importance of the received results consists in generalization of methods of non-equilibrium thermodynamics in expansion of scope DRR on non-linear systems and processes with any degree of dissipativeness in a finding of the diagonal form of laws of transfer in the further reduction of number of kinetic coefficients in them from n (n+1)/2 up to n and in creation of preconditions for development the theory studying kinetics of energy transformation processes.