The legislator established certain features of the emergence of state-service legal relations. For the emergence of these relations, both the act of appointment to the position and the service contract are important. The article deals with the problems associated with the emergence of an individual state-service legal relationship between the state (state body) as an employer and a citizen or civil servant (employed) in the Russian Federation. A distinctive and main feature of the emergence of public-service legal relations between the employer and the citizen (state civil servant) is that the conclusion of a service contract is carried out with a person already appointed to the appropriate position of the civil service on the basis of the issuance of the relevant act of the representative of the employer. At the same time, there is no clear idea of how the parties to a service contract should act when concluding it if there is no agreement in principle between them on a number of conditions, given that the civil servant has already been appointed by the employer to the appropriate civil service position and has begun to perform his direct duties. The authors draw attention to the unsuccessful definition of a service contract in Part 1 of Article 23 of the Federal Law of July 27, 2004 no. 79-FZ “On the State Civil Service of the Russian Federation”, since the representative of the employer cannot be an “employer”, and therefore, cannot be an independent subject of a service legal relationship. The representative of the employer, only implements the functions of the employer, signs a service contract on his behalf. The problems associated with the emergence of a public-service legal relationship and the conclusion of a service contract, to date, remain largely unexplored.