The current paper features the requirements of the labour market for competitive graduates training. The employers' requirements were studied according to the Kano Model method. The author defines general information about the needs of employers in graduates. The interests and capabilities of higher educational institutions were also taken into account. The article represents and analyses the characteristics, skills and quality of a competitive graduate training. Prospective employers identified the following parameters of quality of competitive graduate training: the level of responsibility, the level of practical skills and that of interpersonal skills (communication, negotiation, conflict resolution, teamwork), initiative, etc. The study identifies the skills that employers identify as lacking: practical skills, analytical skills, problem solving, customer relationships, written communication, second-language skills, presentation skills, etc. The paper features the results of a survey conducted and the analysis of the forms of possible cooperation between the higher educational institution and the employer. It represents the factors that influence the decision of employers in the process of recruiting graduates, and the level of satisfaction of the employers.