In this article an attempt to study the particular problems of the providing of criminal justice in the courts of appellate and cassational instances is made. The definition and features of appellate and cassational processes are considered. The author defined a range of questions that may be subject of appellate and cassational complaints. Attention was allotted to powers of courts of appellate and cassational instances. On the ground of this research, the author introduces suggestions for further amendments of the criminal procedure legislation.