As far as the criminal trial is concerned, celerity generally implies both a swift solution of criminal causes, and, if the case may be, a simplified criminal processual activity. At the same time, celerity implies the pursuance of specific activities by the criminal investigation body which has at its disposal the most efficient means for administering evidence. The efficient performance of a criminal investigation (which is a characteristic of the entire criminal trial), though it cannot be regarded as a rule for this trial, is provided by many regulations comprised in the Criminal Procedure Code. As far as criminal trials are concerned, the principle of reasonable time is indissolubly linked with the principle of celerity. From this point of view, the slow judgment of a criminal case infringes upon the right of a person to have his case solved within a reasonable time, which is an essential characteristic of a fair trial. The topic of this paper is not necessarily a particular issue for our national legal system; in fact, it represents a real problem for most national processual systems and this aspect is revealed by the large number of national and international programmes dedicated to the study of the causes which lead to the non-observance of the reasonable time within which a criminal trial should be judged.