Abstract: In long time the problems that sport psychology has faced in the area of professional sports include: 1) which psychological indicators can be used to differentiate training-type from competition-type of athletes? 2) How to define, monitor and control the mental fatigue formed in the long time and intensive training and competitions? 3) What are the necessary mental conditions for getting into the state of peak performance? 4) What are the characteristics of brains’ function during athletes’ peak performance? 5) What are the common attributes and different features in the process of development of self among elite athletes and elite people in other fields? 6) Is there sport intelligence? These six problems were analyzed in line of theory and practice. The approaches to solve these problems were also proposed. It is pointed out that the exploration of these problems will help sport psychology to make contribution to the development of its mother science, i.e. psychology.

Key words: sport psychology, competition, mental fatigue, self, intelligence