The paper deals with problems connected with the premises conditioning the acceptance of a cessation appeal by the Supreme Court, in particular the interpretation and practical use of article 3989 of the Code of Civil Procedure. In the first place, a legal institution called a “przedsąd”, a first stage of the process of examining a cessation appeal by the Supreme Court, is briefly summarized. Subsequently, the author explains questions common to all the premises regulated by article 3989 of the Code of Civil Procedure and the connection between those premises and the grounds for a cessation appeal. Next, the author proceeds to interpret the premises governed by article 3989 of the Code of Civil Procedure and explains how they are put into practice. The last part of the paper contains the author’s conclusions: the premises are strongly connected with the public interest and the development of law; putting them into practice demands a lot of work, even from lawyers.