When you don't appear to have any physical rituals, it seems very logical to assume that you only have obsessions, and no compulsions. This is where the "Pure-O" label originates, in the idea of being purely obsessional. What I have discovered in treatment is that compulsions or rituals that take place in my mind are every bit as real as those that are visible to the rest of the world.
Compulsing is the glue that makes an obsessive thought stick(after the initial hit of relief). It reminds of times I have tried to fix something I perceive as a flaw, and ending up making it worse, because the thought of walking away without trying to get rid of it seems too anxiety provoking. There are some thoughts that if I imagine letting them pass, I get very anxious, because I must make sure they aren't true, or I believe they say something about me as a person.
If I get involved in the battle against them, I lose every time. Going over conversations in my mind, reconstructing what I said, analyzing, ruminating, mental acrobatics. I left a comment on a friend's facebook wall today and suddenly thought "What if this is rude?" and my urge was to try and establish if it was indeed rude, over and over, and in the past I would've gotten stuck on this and lost a chunk of my day, or tried to find a way to see if the other person thought it was rude and on and on.
Other of my rituals actually are physical, but I never thought of them that way. Looking things up on the internet is an actual activity, as is avoiding certain things(for years I didn't watch the news or listen to the radio), or long sessions of writing in my journal analyzing everything.
Once I learned to identify my compulsions, it was easier to figure out what an exposure was, and what "response prevention" means in Exposure and Response Prevention therapy. So today, I accepted that my facebook comment may have been rude, felt some anxiety, and moved on instead of analyzing every angle, and the anxiety moved on as well.