The present invention relates to a method for controlling invertebrate pests, in particular arthropod pests and nematodes, by using pyridine compounds of formulae I or II and the salts thereof, the tautomers thereof, the N-oxides thereof and the salts of the tautomers or N-oxides thereof, where the radical A is of the formula A, wherein # denotes the point of attachment to the remainder of formulae I or II, and wherein A1 is N or C—RA1, A2 is N or C—RA2, A3 is N or C—RA3, A4 is N or C—RA4 and A5 is N or C—RA5, provided that one or two of the variables A1, A2, A3, A4 or A5 is N; RA1, RA5, if present, are H, halogen, CN, NO2, C1-C6-alkyl, C1-C6-haloalkyl and the like; RA2, RA4, if present, are H, halogen, CN, NO2, C1-C10-alkyl, C1-C10-haloalkyl and the like; RA3, if present, is H, halogen, CN, NO2, C1-C10-alkyl, C1-C10-haloalkyl and the like; R1 is H, CN, C1-C10-alkyl, C1-C10-haloalkyl and the like; R2 is H, halogen, methyl, C1-haloalkyl and the like; R3 is H, halogen, C1-C4-alkyl, C1-C3-haloalkyl and the like; X1 is S, O or NR1a, wherein R1a is H, C1-C10-alkyl and the like; X2 is OR2a, NR2bR2c or S(O)mR2d, wherein m is 0, 1 or 2, R2a is C1-C4-alkyl, C1-C4-haloalkyl and the like, R2b and R2c are H, C1-C4-alkyl, C1-C4-haloalkyl and the like, or R2b and R2c together with the nitrogen atom to which they are bound form a heterocycle, and R2d is C1-C4-alkyl, C1-C4-haloalkyl, C3-C6-cycloalkyl and the like. The present invention further relates to a method for protecting plant propagation material and/or the plants which grow therefrom, to plant propagation material, comprising at least one compound of formulae I or II, their salts or N-oxides, and to an agricultural composition containing at least one compound of formulae I or II, their salts or N-oxides.