In the article the approaches to the general theory of systems put by founders of this theory in the sixties of the last century are considered. These approaches are considerably characteristic also of todays submission of the general theory of systems. These approaches can be classified on three conditional groups — mathematical approach to the general theory of systems (M. Mesarovich, Y. Takahara), "physical" approach to the theory of open systems (L. von Bertalanfi, Y. L. Klimontovich) and approach on the basis of functional systems (P. K. Anokhin). The approaches offered by authors to further development of the general theory of systems and its practical application are considered.