This paper presents the main results obtained from 40 in-depth interviews with persons in charge of human resources and/or company directors, and from a questionnaire targeting 872 companies surveyed from a data base of the 5,000 main Spanish companies. The objectives of this paper are the following: first, to identify the competencies required of university graduates by the labour market; second, to find out the mismatches that may exist between the current higher education students receive and company demands; and third, to discover how and to what extent universities can improve their education and training in order to reduce the gap that, according to employers, exists between current business needs and the education that graduates have upon entering the labour market. To carry out this research project, the competencies under study have been divided into two large groups: vocational and generic. At the same time, the latter have been subdivided into three subgroups: knowledge-related, methodological, and interpersonal competencies. (Contains 1 table and 1 note.)