The present invention relates to novel pyridylmethyl-sulfonamide compounds of formula (I) where: n is 0 to 4; m is 0 to 4; R1 is halogen, CN, NO2, OH, SH, C1-C4-alkyl, C1-C4-haloalkyl, C1-C4-alkoxy, C1-C4-haloalkoxy, etc.; and/or two radicals R1 together form a fused ring; R2 is H, C1-C4-alkyl, C1-C4-haloalkyl, C2-C4-alkenyl, C2-C4-alkynyl, C3-C8-cycloalkyl, C1-C4-alkyl-C3-C8-cycloalkyl or benzyl; R3 is halogen, CN, NO2, C1-C4-alkyl, C1-C4-haloalkyl, C1-C4-alkoxy or C1-C4-haloalkoxy; Y is —O—, C1-C4-alkanediyl, —O—CH2—, —CH2—O—, —C(NORn)—, —S—, —S(═O)—, —S(═O)2— or —N(Rn)—; and the N-oxides, and salts thereof and their use for combating phytopathogenic harmful fungi, and also to compositions and seed comprising at least one such compound.