Postmodernism; Comedy; Family Drama
On the surface, this play is a straight-up comedy. There are tons of laughs to be had in the way these characters all run around having sex with random people. And certainly Cloud 9 has a comedy's traditional happy ending.
But beneath that, Churchill is also telling a few other, darker stories: the story of the young man who's rejected by his parents for being gay, and the story of a wife who spends the majority of her life repressing her sexuality and her individuality. When you consider how much misery these family members have to live with you begin to appreciate how Churchill's comedy also has the upsetting undertones of a family drama.
But the most notable genre that the classification-defying Cloud 9 falls into is Postmodernism. Postmodernism, as our handy-dandy Shmoop Literature Glossary will tell you, is literary shorthand for "quirky." And, uh, yeah, Cloud 9 is quirky. Churchill uses a lot of techniques in this play to confuse our sense of time and place, the most obvious of which is the huge time shift from colonial Africa to modern-day England between Acts 1 and 2. On top of that, Churchill likes to use a lot of cross-dressing to constantly make us question the assumptions we tend to make when we label someone as male or female.
When audience confusion is part of the grand project of a literary work, you just know that you're in Postmodernism territory.