It is commonly accepted that voluntary active euthanasia and physician-assisted suicide can be allowed, if at all, only in the cases of patients whose conditions are incurable. Yet, there are different understandings of when a patient's condition is incurable. In this article, I consider two understandings of the notion of an incurable condition that can be found in the recent debate on physician-assisted dying. According to one of them, a condition is incurable when it is known that there is no cure for it. According to the other, a condition is incurable when no cure is known to exist for it. I propose two criteria for assessing the conceptions and maintain that, in light of the criteria, the latter is more plausible than the former.