Some people—notably, St. Thomas—think that you can have real dilemmas, ones where you are obligated to do each of two incompatible actions, but only when you've done something wrong. For instance, one might make incompatible promises to two different people, and then have a real dilemma, but of course it's wrong to make such incompatible promises.
But given the binding force of conscience, this is not a stable position to hold. For consider a situation S where one would be in a real dilemma, say the situation where one made incompatible promises to two different people. But now imagine a situation S* which is epistemically like S and where the same actions are open to one, but where one did nothing wrong to get into S*. Maybe one has a justified false belief that one has made incompatible promises to two different people (say, a bad friend convinces you that you made such promises but forgot about them). Then while one does not have duties of promise to do the two incompatible actions, one does have duties of conscience to do them.
A complete denial of real dilemmas is a more stable position, as is the position that where there is a real dilemma, something has gone wrong morally or epistemically (but not necessarily through one's having done anything wrong, morally or epistemically).