No seasons. The occasional cougar wanders through Illinois. Once in a while, one ends up dead (hit by a car or train; one was shot in the northern suburbs of Chicago a few years back). But, I think you'd be hunting a long time if you set out to kill one around here. There's just not that many around -- yet. (We get the occasional wolf wandering down from Wisconsin, and at least one bear, but they are few and far between).