The invention relates to 2-cyano-3-(halo)alkoxy-benzenesulfonamide compounds I ##STR00001## where the variables Alk and R.sup.1 to R.sup.5 are as defined in claim 1, and/or to their agriculturally useful salts.Moreover, the present invention relates to the use of compounds I and/or their salts for combating animal pests; agricultural compositions comprising such an amount of at least one compound of the general formula I and/or at least one agriculturally useful salt of I and at least one inert liquid and/or solid agronomically acceptable carrier that it has a pesticidal action and, if desired, at least one surfactant; and a method of combating animal pests which comprises contacting the animal pests, their habit, breeding ground, food supply, plant, seed, soil, area, material or environment in which the animal pests are growing or may grow, or the materials, plants, seeds, soils, surfaces or spaces to be protected from animal attack or infestation with a pesticidally effective amount of at least one 2-cyano-3-(halo)alkoxy-benzenesulfonamide compound of the formula I and/or at least one agriculturally acceptable salt thereof. a method for the for the protection of seeds from soil insects and of the resulting plant's roots and shoots from soil and foliar insects comprising contacting the seeds before sowing and/or after pregermination with a 2-cyano-3-(halo)alkoxy-benzenesulfonamide compound of the general formula I.