The current theories of animal personality are based on the observation that individual variation in behavior and physiology appears to be consistent across contexts. Rats of the Roman selection lines have been originally selected for differences in shuttle-box behavior. Besides differences in active avoidance, these animals differ more generally in coping style. Roman high avoidance (RHA) rats show high levels of active avoidance, whereas Roman low avoidance (RLA) rats tend to respond with a more passive (i.e. freezing) response. Based on the two tier model of coping styles, we hypothesized that RHA rats would show high levels of offensive behavior and are more impulsive compared to RLA rats. We characterized animals in a two-way active avoidance task on five consecutive days. Thereafter animals were tested for their level of offensive aggression and impulsive behavior. The level of offensive aggression was examined in a standard resident-intruder paradigm. Furthermore, we tested aspects of impulsivity in an unpredictable operant conditioning paradigm (variable interval-15 schedule) for food reinforcement and during extinction of lever press behavior. We show that RHA rats are indeed characterized by high levels of two-way active avoidance in a shuttle-box paradigm. Surprisingly, the level of offensive aggression was higher in RLA compared to RHA rats. Consistent with the coping style interpretation, the number of lever presses in the VI-15 schedule for food reinforcement was higher in RHA rats compared to RLA rats. During a session of frustrating non-reward, RHA rats were more persistent. Taken together, results of the two-way active avoidance task and VI-15 performance in rats of the Roman selection lines fit with the two tier model of coping styles. Unexpectedly, the level of offensive aggression does not match with this model.