In the context of globalization, an international market for educational services has emerged. International demand has come into conflict with country differences in supply. The choice of the procedure for knowledge assessing determines the whole system of the organization of the educational process. Two types of exam procedures are analyzed in the article. The first one is typical for United States universities, namely: the exam with the right to pass exams ones more only after re-training. The second is typical for Russia: student has the right to take the exam again twice in case of failure of the first attempt. The first kind leads to the appearance of number of re-learners, which makes it impossible to fix the number of years of study. Each student has his own number of years of study and an individual schedule. Such a subject-based training system differs from the time-limited system suitable for the examination procedure of the second type with the dismissal of students who failed the exam. The article compares the positive and negative aspects of these two systems and shows the possibility of constructing on their basis a more positive model that incorporates their advantages. The results of the socio-psychological research carried out by the authors show the preferences of the students of Russian universities to the second type of examination. Students prefer be expelled from the university, if failing three attempts to pass the exam to alternative to be re-trained. The reasons for this choice are two: significant loss of time for re-training and money for tuition and the suspicion that the university will specifically create conditions for failure to earn on re-training.