An appeal to the concept of the right to a ‘fair trial' and its elements such as jurisdiction and composition of the court reveal itself more and more often in recent times. Some authors, especially in foreign literature, refer to this right as the right to a due process of law. The criminal procedure legislation of the Russian Federation provides for its effect in time. This article represents an attempt to solve the issues of exercising the right to a ‘fair trial' in accordance with the rule of law in time. At the same time, unlike criminal law, the new criminal procedure law has no retroactive effect. The judicial practice on this issue has also changed; its comparative analysis will apparently assist in working out the correct opinion on this issue. Besides, not only changes in the procedural laws affect the determination of the jurisdiction of a particular criminal case but also changes in the criminal and other laws. In this instance, the specified rule of the law in time is applied in each case in different ways. In this article, we will try to reveal and comprehend this difference not only based on a comparison of legislation but also using samples of judicial practice.