This doctoral thesis discloses the research results of copper-catalyzed intramolecular and intermolecular N-arylation of O-alkyl hydroxamates. The recent data about transition metal-catalyzed N-arylation of the hydroxylamine and hydrazine derivatives, sulfur-nitrogen bond containing compounds as well as the methods for synthesis of cyclic N-alkoxy-N-arylamides are summarized and analyzed in the literature review. For the first time the synthesis of N-aryl-O-alkylhydroxamates under copper-catalysis were achieved and new methods for the synthesis of N-alkoxyindol-2-ones and N-aryl-O-alkylhydroxamic acid derivatives have been developed. It was shown, that elaborated methods are applicable to a broad range of substrates and tolerate various functional groups. Thesis was written Latvian; it consisted of 119 pages, 49 schemes, 16 tables, 12 pictures and 180 references