The current research aims to identify the fast-slow thinking style prevalent among university students. It also aims at identifying the level of cognitive failure of university students. Finally, it aims to identify the relationship between the slow and slow thinking and the cognitive failure of university students. The research was determined by the students of the University of Baghdad / morning study of males and females in the scientific and humanitarian disciplines for the academic year (2016-2017). In order to achieve the objectives of the research, the researcher chose a sample of the students of the university and consisted of (400) students from the University of Baghdad and were selected in random way multi-stage. The statistical methods adopted the Pearson correlation coefficient, the test for one sample. The research found results that indicate a relationship between cognitive failure and rapid thinking. Finally, in light of the results of the research, a number of recommendations and proposals were developed.