Purpose: Available literature overlooks the factors that affect employers' opinions of the skills graduates bring to the labour market. The purpose of this paper is to examine the relationship between the perception of graduates' skills and the employers' anticipative and remedial strategies. Design/methodology/approach: A qualitative multiple case study is used and data were gathered from interviews with human resource managers in ten firms in Portugal. The data set includes information on perceptions of graduates' skills, solutions for the acquisition of skills, hiring and training policies, and practices associated with university-industry linkages. Findings: Almost all the employers sampled are unsatisfied with graduates' preparation in soft skills and other personal traits. Some report skill shortages and gaps in technical skills that result in training costs. The perception of technical skills varies according to anticipative and remedial strategies. Research limitations/implications: This is an explorative study with a very small sample of firms. However, it is a first step towards further research into whether the perception of graduates' skills is affected by anticipative and remedial strategies implemented by firms within a particular human resource development system. Practical implications: It is argued that the responsibility for graduates' employability should be shared. Practitioners should learn how to interact with higher education, researchers should profit from insights into typologies of employers' strategies on skill formation, and policy makers should understand that employers are heterogeneous and there is no one-size-fits-all solution. Social implications: Universities, employers and policy makers should understand that the employability of graduates presupposes shared responsibility. Originality/value: The relationship between the strategies employers adopt to access skills and their perception of graduates' skills is a quite underexplored topic.