This paper investigates how power and hegemony are embedded in legal-diplomatic discourse, particularly in the UN Security Council (UNSC) resolutions and the International Court of Justice (ICJ) decisions on armed conflict and proliferation of weapons. Based on Genre Analysis and CDA, particularly Bhatia's (1993) Move Analysis model and Fowler's (1985) checklist, this paper analyses the move-structure and the syntactic and stylistic features of such documents so as to unveil how selecting certain linguistic patterns and organising information structure in a specific way represent power and hegemony in these texts. It also examines the similarities and differences between the UNSC resolutions and the ICJ decisions. The data chosen are 24 UN documents on armed conflict and the proliferation of nuclear weapons within the period of 2015 to 2017; nine of them are of the ICJ decisions and fifteen are of the UNSC resolutions and they are collected from the United Nations official website (www.un.org/en/documents). The findings show that power and hegemony of the UNSC resolutions and the ICJ decisions are reflected in certain linguistic choices at word, sentence, and textual level, most notably long complex clauses, modal verbs, technical, foreign, and archaic vocabulary, etc. Such tools make such documents appear as only one sentence long, composed of a number of paragraphs separated by comma and semicolon. Additionally, such documents are divided into three moves: identifying the case/resolution; arguing the case, which includes two sub-moves: presenting arguments and deriving ratio decidendi; and pronouncing judgement/declaring the resolution. Finally, it is observed that the UNSC resolutions and the ICJ decisions have great similarities regarding the move analysis and the linguistic features with some little differences.