The subject of this study is some shortcomings of the legal regulation of employment relations. An employment relationship with a given employer is understood as a relationship mediated by the employment service, as well as direct interaction between a candidate and an employer on employment issues. The article discusses the general aspects of the regulation of selection procedures by the employer, the use of psychophysiological research in the selection of candidates, as well as the existing practice of job offers. Consideration of these issues is relevant due to the lack of labor law regulation of the relevant relations. The purpose of the study is to formulate specific proposals for amendments to labor legislation in order to regulate polygraph testing and the practice of making job offers. When writing the article, the formal logical method was used, as well as methods of systematic and literal interpretation of legal norms. The result of the conducted research are proposals for regulating polygraph testing in employment (verification is carried out at the expense of the employer; with the written consent of the candidate for work; the range of questions asked and the research methodology are subordinated to the purpose of checking the business qualities of a potential employee; the conclusion based on the results of the study cannot be an independent basis for refusal to apply for a job). Proposals on the legal regulation of the job offer are also formulated, concerning its form, content, and options for interaction between the candidate and the employer in various situations. If the terms of the job offer and the terms of the concluded employment contract do not match, priority should be given to those conditions that are more favorable for the employee. In case of non-conclusion of an employment contract, it is proposed to assign the obligation to reimburse expenses incurred by the bona fide party to the employment relationship to the other party.