Pursuant to Art. 982 of the Civil Code "the testator, in a will, may impose on a heir or legatee the obligation to carry out a specific action or to refrain from carrying out of specific action without making anyone a creditor (testamentary burden)". The institution of testamentary burden allows the testators to produce legal effects mortis causa which achieving would not be possible in the way of other testamentary disposals (for instance legacy). This paper relates to testamentary  burden (done in the public interest), the fulfillment of which may be demanded – apart from testator and last will executor – also by a competent State agency (Art. 985 of the Civil Code). Author defines the notion of the competent State agency. This notion raises interpretation doubts as the  principle of the uniform system of state power was given up. Furthermore, he discusses the issue of the prosecutor’s right of action to demand the fulfilment of the testamentary burden. The author also states de lege ferenda comments, based on the analysis of the institution of the testamentary burden in German, Swiss and Austrian law according to which the notion of "a competent State agency" should be replaced with the notion "a competent authority".