As governments and international organisations have pressured universities to demonstrate the value and effectiveness of tertiary education, universities have started to highlight graduate employability as a key driver and measure of university outcomes. This paper contributes to the underutilised "processual" employability studies by applying the framework of critical discursive psychology to analyse university students' employability construction. Following this framework, employability is something students "do" rather than something they "have." The empirical study was based on interviews of Finnish students of social science. Analysis of the interviews demonstrated notable variation in the ways in which university students talk about their employability. While some students constructed their employability by positioning themselves as traditional bureaucrats, others constructed their employability by positioning themselves as entrepreneurial agents. Nevertheless, the central point is that some students related ambiguously to both positions and tried to manage the ideological dilemma between stability and security of the bureaucrat position, and variability and risk of the entrepreneurial position. The study calls for better understanding of ways in which students and graduates deal with the dilemmatic nature and requirements of the labour market.