To remove sulfur-containing compounds (SCC) from the diesel fraction 200–360 °C extraction systems have been created based on coordinating organic solvents—dimethylformamide and dimethylsulfoxide, metal chlorides (CoCl2, CuCl2, CdCl2, MnCl2 and CrCl3), and metal trifluoroacetates (Co(TFA)2, Cu(TFA)2 and Mn(TFA)2). Using PMR spectroscopy the coordination of metal chloride and metal trifluoroacetate on the oxygen atom in the carbonyl group of DMF was shown to redistribute electron density in the solvent molecule and to enhance properties of the acceptor center localized on the nitrogen atom. The removal of sulfur-containing compounds from the diesel fraction proceeded under mild conditions—at the temperature of 25 °C and atmospheric pressure. The degree of SCC removal from the diesel fraction in 30 minutes extraction was more than 90%. The interaction of organic solvents with metal salts and sulfur-containing compounds of the diesel fraction was considered within the framework of the concept of “hard and soft acids and bases” (HSAB). The most complete SCC extraction was carried out with DMF-Mn(TFA)2, MnCl2 and CrCl3 systems, that was probably connected with the implementation of the ‘hard base–hard acid’ system.