We describe a novel two-step approach for the synthesis of compounds with a hydroxyl-amide group (hydroxamic acids), which are widely known for their biological activity (histone deacetylase inhibitors, matrix metalloproteinases inhibitors and others). The first stage is the synthesis of N-substituted succinimide via the reaction of aromatic amine or carboxylic acid hydrazide with succinic anhydride. The second step involves the imide ring opening reaction by hydroxylamine. For both stages, universal synthetic methods are developed to exclude additional purification procedures for the target compounds. Sixteen hydroxamic acids are synthesized using the developed approach. Most of the compounds are obtained for the first time.