Each human group and each society is a complex system of cooperative and competitive relationships. These two relations are intertwined, however, it is not indifferent in what way and to what extent. The present research has aimed at revealing the requirements of cooperative competition which is a competitive process with a high degree of cooperation among the competing parties. The Critical Incident Technique was applied. This procedure is based on the direct observation of human behaviour and was elaborated in order to examine complex interpersonal phenomena and to provide ecological validity. Altogether 483 critical incidents were described by teachers and university students of education. They were instructed to recall competitive relationships that have certain characteristics (e.g. high degree of cooperation among the parties vs no cooperation among the parties; high degree of trust among the parties vs high degree of distrust among the parties, etc.) After the free description of the incident, the participants had to characterize the competitive event along different dimensions on a Likert-scale, for instance intense/not intense competition; rules kept or violated. Applying principal component analysis, four different scales were constructed: the Cooperation Scale (i.e. the relationship among the competitors, cooperation, trust and communication), the Motivation Scale (i.e. motivation, the importance of the goal, development and learning), the Fairness Scale (i.e. rule keeping, no aggression and no manipulation) and the Enjoyment Scale (i.e. enjoyment and positive stress). The correlation analysis of the interrelations among the scales and individual variables has indicated that the high degree of cooperation among the competitors was positively related to fairness, the clarity of rules of competition, enjoyment and motivation. Less cooperation among the competitors was related to higher level stress and more intensive competition among them. If competitive processes are characterized by high degree of cooperation, i.e. they are cooperative competitions that have no detrimental but only beneficial effects, then they combine the constructive aspects of both cooperation and competition.