In the present paper the authors raise the question about competition of social and economic rights with respect to labor relations. It is used set of research methods including both general scientific (dialectic, analysis and synthesis, abstraction and concretization) and special scientific methods (formal-legal, technical-legal). It is noted that the specifics of labor relations and legal status of their entities predetermined the possibility of competition of the social rights of employees and economic rights of the employer. In particular the problem of competition of social and economic rights of subjects of labor relations arises during implementation by the employer his powers of labor management. On based of the goals and objectives of the labor legislation it is stated that the competition of social and economic rights of subjects of labor relations should be resolved on the basis of the balance of the constitutional rights and freedoms of workers and employers. The authors provide examples the rules on dismissal of employees due to downsizing and its show that the relevant legal framework as a whole provides a resolution of the problem of competition of social and economic rights of subjects of labor relations but at the same time it is needs to be further improved.