Although nearly three years have elapsed since the publication of this work in Hungarian, it was decided to publish the English edition in the same form as the original, apart from some minor modifications. Since, recent research has been directed to the development of an exact theory of non-linear irreversible processes; we suggest to readers interested in similar tasks - such as the continuation of this boo- that they should study some new publications: "On the most general form of the Thermodynamic Integral Principle," Z. phys. Chem. 239 (1968) 133, and particularly: "On the Governing Principle of Dissi pative Processes," Ann. Phys. 7 (1969) 23. I have to thank my wife and Mr. W.F.HEINZ for the translation of the very concise Hungarian text. I also wish to express my gratitude to Dr. L.KARADI and Mr. Gy. VINCZE for reading the typescript with such care and to Mrs. A. R6sZLER, who typed the manuscript with great patience. I am deeply indebted to Professor ISTVAN SZABO for making this edition available so quickly and for including my work in the "En gineering Science Library." Finally, I would like to express my thanks to Springer-Verlag for the excellent edition and to the editorial staff for their readiness to meet my wishes."