In this paper, we discuss the use of formal requirementsengineering techniques in capturing security requirements for a Grid-based operating system. We use KAOS goal model to represent two security goals for Grid systems, namely authorisation and single-sign on authentication. We apply goal-refinement to derive security requirements for these two security goals and we develop a model of antigoals and show how system vulnerabilities and threats to the security goals can arise from such anti-models.