Sulfonamides of the formula I ##STR00001## where the substituents are as follows: R.sup.1 is hydrogen, alkyl, alkoxy, alkenyl or alkynyl; and R.sup.2, R.sup.3, R.sup.4, R.sup.5 are hydrogen, halogen, alkyl, alkoxy or halomethyl; R.sup.2 and R.sup.3 together may also form a phenyl, cyclopentyl or cyclohexyl ring, it being possible for these rings to carry two groups R.sup.2, and R.sup.3, R.sup.2, R.sup.3, are hydrogen, halogen, alkyl, alkoxy or halomethyl; in case a), if R.sup.2, R.sup.3, R.sup.4 and R.sup.5 are hydrogen: X is phenyl substituted by a group --C(R.sup.6).dbd.NOR.sup.7, where R.sup.6 is alkyl and R.sup.7 is alkyl, benzyl, alkenyl, haloalkyl, haloalkenyl, alkynyl or haloalkynyl; and in case b), if at least one of the groups R.sup.2, R.sup.3, R.sup.4 and R.sup.5 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.