Offhand I would expect cycles to be possible; why not? In the extreme case, if I cast Imperius on you, then your desries will follow mine, and if (through some perversity) I desire you to cast Imperius on me, then you'll do it.

Among trusted friends, this could be a nice way to get high (well, mellow) for a while. Then eventually I will you to lift the curse on me, then lift my curse on you (or the other way around). It could also work for willpower, even if you can't cast it on yourself. (Aside unrelated to acylcicity: the Ministry could license some well trained, closely supervised Wizarding therapists to use Imperius to treat addiction and the like.)

If you know that you're in a cycle and want out, then it's easy to get out. Just will someone to will someone to … will someone to lift the curse on you. But you might not know.