The new legal and historical context of the imminent prospect of Republic of Moldova's integration into the European Union obliges the development, adoption and application of qualitative and significant legal acts, the objectives seted in the Reform Strategy of the Justice Sector for the years 2011-2016 on simplification and streamlining criminal proceedings being very important in this matter. In order to support the achievement of the mentioned objectives, in this article we bring into atention the issues related to the degrees of the jurisdiction in the trial of criminal cases, which remains very important. In this context, we expose a view to identify and develop the best solutions for resolving legal issues related to the degrees of the jurisdiction in the appeal criminal cases, so to be helpful for the legislative branch and jurisprudence.