The aim is to devise a model of integral development of antagonistic physical qualities in sports that require complex manifestation of motor abilities.Materials: there were analyzed 32 literary sources for devising the theoretical theses of a model of development of different physical qualities.The elite climbers took part in the pedagogical experiment in order to test the effectiveness of the developed model.There were 26 sportsmen involved in the study (among them were 10 sports masters of international class who specialize in speed climbing, 10 sports masters who specialize in difficulty climbing and 6 world-class climbers.The age of sportsmen was from 19 to 22. Results.We developed the concept of an integrated physical training.It, in general, can be applied at any stage of sports perfection.It was found that the components of physical preparedness (strength, speed and endurance) are in inverse interrelations.The data of dependences are hyperbolic.We demonstrated these dependencies (between strength, speed and time limit of acting) are, in generalized form, in the shape of a hyperboloid.We also showed that the inverse interrelations between the components of speed and strength preparedness make difficulty in building of training process.The solution of this problem lies in the gradual alternation of means aimed at the development of contradictory qualities.Conclusions.We proved experimentally the effectiveness of the developed model of integral development of physical qualities in training process of elite climbers.