In the Serbian literature the issue of the overlap between contractual and liability in tort has been thoroughly discussed. The majority of references state that the differences between the two regimes of liability outweigh their common features, thus separate sets of rules should exist governing each. There are authors who claim that differences are not of such significance so as make the integral concept of liability for damage senseless, hence they support the idea of regulating both regimes of liability by a single set of rules. The effective Obligations Act of 1978 is in line with the majority opinion, since it envisages different sets of rules for each regime of liability. Taking into account the existing duality of the rules in the Act, which significantly differ on major points, the key issue is the overlap of contractual and tortious liability, namely rules of which system of liability should apply if the injured party may base their claim on both (so-called concurrency of claims). Lacking an explicit rule in the Obligations Act, the majority asserts that the regime more favorable to the injured party should apply, which corresponds to the German solution. The inspiration for this paper is found in the new Hungarian Civil Code from 2013 which, in contrast to its predecessor, the 1959 Civil Code, and the Serbian Obligations Act, contains an explicit rule on the concurrency of claims in contract and tort. It prescribes a mandatory application of the rules of contractual liability even when the inflicted damage supports the application of the rules of the liability in tort. Such an approach is in line with the French non-cumul doctrine. The aim of this paper is, on the one hand, to initiate a discussion whether it would be reasonable to have a statutory rule in the Serbian law regulating explicitly the issue of concurrency of claims in contract and tort. On the other hand, the paper highlights the reasons that led the legislator in Hungary to prohibit the concurrency of claims. The solution of the new Turkish Code of Obligations from 2011 is mentioned in the paper, as well, which also contains an explicit rule on this subject matter. However, it took a diametrically opposite standpoint as the Hungarian Civil Code: it explicitly enables competing claims not only in contract and tort, but according to any set of rules granting redress to the injured party. Finally, the paper gives a review of the Project of the Reform of the French Code Civil concerning the rules of the liability for damage from 2017. The Project envisaged a rule that would codify the traditional standpoint of the case law and doctrine on the exclusion of the concurrence of claims and mandates the application of the rules on contractual liability. The Project specifies, however, some major exceptions, when regardless of the existence of a contract between the parties, the rules of tortious liability apply. For the time being, however, it seems that a genuine will of the legislature is lacking to embody the Project in the amendments of the Code civil.