This article researches higher education (HE) managers' perception of graduate professional success and higher education institutions' (HEI) activity aimed at enhancing graduate employability. The issue is worth examining not only because of growing relative unemployment rates among HE graduates but also because it is a part of a heated discussion on the contemporary evolution of HEIs. We analysed 36 semi-structured interviews with representatives of HEIs offering studies in the field of science in six countries (Austria, Germany, Italy, Poland, Slovenia and Turkey). Our analysis showed that there are three approaches observed, depending to a large extent on the balance between different HE stakeholders within subdomains (triple-helix theory). Our results support the hypothesis of diversification of HEIs' models varying from the traditional ivory-tower-type university (with a dominating role of academic oligarchy) to the market-oriented educational enterprise (where the business sector is a key driver of change).