The study focuses on the labour-market situation of young graduates utilizing the database of the Hungarian Graduate Tracking System. The purpose of the research is to map certain characteristics of the precarious situation posed by the labor market on this group which is in a rather favorable labor market position in comparison to other groups. The concept of the precariat is defined as a type of labor-market uncertainty, in which unfavorable working conditions, like insecure short-term jobs, fixed-term employment contracts, low wages, etc. are concentrated. In addition to the lack of financial security, these characteristics may lead to general insecurity and in some cases to labor market and social exclusion (LaVaque-Manty 2012, Standing 2012). This analysis focuses on the presence of a precarious condition that creates an insecure labour-market situation among young graduates and it attempts to find the main explanatory variables in the interpretation of this phenomenon. In addition, it investigates whether socio-demographic, socio-cultural characteristics, like gender, marital status, type of qualification (BSc, MSc, or Ph.D. degree), and the type of settlement (village, town, city, etc.) affect success in the labour-market. Preliminary results support previous studies that found women in the labor market were disadvantaged. For example, the proportion of women with a fixed employment contract is higher than men, and the interruption of a labor market career is more characteristic of women. More women gave a positive answer to ”I am not working at the moment although I have previously had a workplace”. This suggests that women are more affected by a less stable and less secure labor market than men.