Absolute stability theory is an important and historically the first systematic part of automatic control theory. The ideas and methods developed by its founders influenced subsequent development of nonlinear control, robust control, etc. In this paper the early ideas of the absolute stability and their development are outlined. Most attention is paid to the results born in St. Petersburg (Leningrad) in the 1940s-1960s, since the author knows this area better. The development of the absolute stability theory during those years was primarily associated with the names of outstanding scientists Anatoly Lurie, Efim Rosenwasser, Vladimir Yakubovich, whose results are addressed more often.