The paper discusses some possible generalization of the Popperian demarcation criterion. Proponents of various theoretical schools, argues the author, tend to present their views as new and groundbreaking, and to obtain that effect they concentrate only on arguments that support their theory. They are guided by the conviction that their opponents will not help them to find confirming evidence, and in most cases it is probably true. But one should not hope that they can be more critical to their own theory. It is reasonable to make some allowance for the human nature-one cannot be very efficient when placed in two roles at the same time, that of proponent and that of the opponent of the same theory. It is more promising, therefore, to direct the appeal for criticism only to the opponents of the theory that has been presented. The author discusses this proposal in some detail and gives it a formal interpretation, too.