Sulfonamides of the formula I where the substituents are as follows: R1 is hydrogen, alkyl, alkoxy, alkenyl or alkynyl; and R2, R3, R4, R5 are hydrogen, halogen, alkyl, alkoxy or halomethyl; R2 and R3 together may also form a phenyl, cyclopentyl or cyclohexyl ring, it being possible for these rings to carry two groups R2′ and R3′, R2′, R3′ are hydrogen, halogen, alkyl, alkoxy or halomethyl; in case a), if R2, R3, R4 and R5 are hydrogen: X is phenyl substituted by a group C(R6)═NOR7, where R6 is alkyl and R7 is alkyl, benzyl, alkenyl, haloalkyl, haloalkenyl, alkynyl or haloalkynyl; and in case b), if at least one of the groups R2, R3, R4 and R5 is not hydrogen: X is phenyl, naphthyl or a five- or six-membered saturated, or partially unsaturated or aromatic heterocycle which is attached via a carbon atom and contains one to four heteroatoms from the group consisting of O, N and S, where X may be substituted according to the description; Processes for preparing these compounds, compositions comprising them and their use for controlling phytopathogenic harmful fungi.