The open field (OF) is thought to induce anxiety in rodents. It also allows an opportunity for exploration in a novel environment. Less activity in the OF is thought to indicate greater anxiety whereas more activity may reflect greater exploration, and possibly greater exploratory learning. Anxiety and learning have poorly understood relationships to sleep. In order to determine how anxiety and exploration in the OF could influence sleep, we recorded sleep in mouse strains (C57BL/6J (B6), BALB/cJ (C), DBA/2J (D2), and CB6F1/J (CB6)) with different levels of anxiety and exploration after 30 min in an OF. In all strains, OF exposure induced immediate decreases in rapid eye movement sleep (REM) followed by longer latency increases in REM. The time course and amount of REM decreases and increases varied among strains. Compared to less anxious B6, D2 and CB6 mice, C mice had greater and longer lasting immediate decreases in REM. C mice also displayed longer periods of decreases REM and a smaller, longer latency increase in REM. OF exploratory activity was positively correlated to percentage of REM increases from 6 to 10h after OF exposure. The results suggest that the anxiogenic component of the OF produced an immediate decrease in REM that was greater in more "anxious" mice. In contrast, exploration in the OF was associated with increased REM, with the increase greater in less anxious mice. The results are discussed with respect to the potential influences of anxiety and learning on sleep.