Grid systems are designed to support very large data set computations, that potentially access significant resources spread through several organizations. These resources can be very tempting for a hacker because they can be used, for example, to break pass-phrases with brute-force attacks or to launch distributed denial of service attacks to a given target. In this paper, we explain how malicious intrusions can be tolerated in the Globus toolkit grid environment, a de facto standard in this area.