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The main role of public administration is to administrate public affairs. All of the functions in  this field are realised by  employees carrying out the dependent work. Public administration, as  an employer, has to  fulfil the demand of  stability and attractiveness of public sector employment. For the purposes of the study our attention focuses on a large group of public employees, namely teachers in public universities in Slovakia. Legislative regulation of the employment of university teachers is alarming. The paper analyses Slovak legislation of time-terminated employment contracts with university teachers and its unlimited repetition. The authors, supported by settled case law of the Court of Justice of the EU, assess the legislation in substance and critically, but also point to its potential impact on the private life, social security and health of these employees, i.e. psychological aspects. Descriptive analysis aimed at assessing quantitative changes in individual groups of university teachers according to the highest level of qualification was used to express trends in the development of quantitative indicators characterizing selected aspects of employment of university teachers (assistant, assistant professor, associate professor, professor). Legislation on the employment of university teachers under the conditions of the Slovak Republic raises considerations of  unequal treatment of  two categories of  university teachers (associate professors and professors) when compared to the category of assistants and assistant professors. For this reason, an analysis of the age structure of university teachers according to the highest qualifications was carried out. The analyses were carried out using data from the Center of Scientific and Technical Information of the Slovak Republic (CVTI SR) and the Register of University Employees maintained by the Ministry of Education, Science, Research and Sport of the Slovak Republic. The study was conducted for the reference term of 2011–2019. Through our analysis, we have identified a downward trend in  the number of  university teachers qualified as  assistant professors in  the 40–49 age category, and this change does not reflect the increase in the number of associate professors in the same age category. The group of university teachers in this age category then becomes vulnerable/disadvantaged in the labor market, which has serious social consequences for the employees themselves and provides a picture of the university environment in terms of legislation.