Alternative forms of concluding a criminal proceedings represent a legal novelty in a number of modern criminal codes in the world. In this regard, Libya joined the countries which had legalized the alternative way of ending a criminal proceedings. In such a way there is achieved a multiple legal effects in the area of respecting fundamental criminal procedure principles, such as: economy, efficiency, equity and others. Although a certain part of the criminal theory challenges this way of concluding a criminal proceedings, there is an opinion prevailed according to which the realization of the aforementioned principles contributes to the timely solution of a certain criminal matters. A prerequisite for such an ending of a criminal proceedings is making a decision concerning the non-prosecution brought by the public prosecutor in order a particular criminal case to be solved in an alternative way (by using a method of settlement). Starting from the previously mentioned facts, the author of this paper has come to an idea the decision on the non-prosecution brought by the public prosecutor to be treated from a theoretical standpoint including, in certain segments, his own experience working as a prosecutor in Libya. In this sense, this paper represents a synthesis of both theory and practice in the light of existing solutions in the Libyan criminal law.