The present invention relates to novel benzenesulfonanilide compounds of the formulae I and I′ and physiologically tolerated acid addition salts and the N-oxides thereof. The compounds possess valuable therapeutic properties and are particularly suitable, for treating diseases that respond to modulation of the serotonin 5-HT6 receptor. wherein R1 is hydrogen or methyl; R2 is hydrogen or methyl and is positioned vicinal to the radical R1; R3 hydrogen, C1-C3 alkyl, halogen, C1-C3 alkoxy, fluorinated C1-C3 alkyl or fluorinated C1-C3 alkoxy; R4 is hydrogen, C1-C4 alkyl, C3-C4 cycloalkyl, C3-C4 cycloalkylmethyl or fluorinated C1-C4 alkyl; R5 is hydrogen, fluorine, chlorine, C1-C4 alkyl, fluorinated C1-C4 alkyl, C1-C4 alkoxy or fluorinated C1-C4 alkoxy; and R6 is hydrogen, fluorine or chlorine.