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This paper describes COMET, a collaborative intelligent tutoring system for medical problem-based learning. The system uses Bayesian networks to model individual student knowledge and activity, as well as that of the group. It incorporates a multi-modal interface that integrates text and graphics so as to provide a rich communication channel between the students and the system, as well as among students in the group. Students can sketch directly on medical images, search for medical concepts, and sketch hypotheses on a shared workspace. The prototype system incorporates substantial domain knowledge in the area of head injury diagnosis. A major challenge in building COMET has been to develop algorithms for generating tutoring hints. Tutoring in PBL is particularly challenging since the tutor should provide as little guidance as possible while at the same time not allowing the students to get lost. From studies of PBL sessions at a local medical school, we have identified and implemented eight commonly used hinting strategies. We compared the tutoring hints generated by COMET with those of experienced human tutors. Our results show that COMET's hints agree with the hints of the majority of the human tutors with a high degree of statistical agreement (McNemar test, p = 0.652, Kappa = 0.773).