The present invention relates to pyridazine compounds of formulae I or II and the salts thereof, the N-oxides thereof and the salts of the 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; where W is N or C—RW and V is N or C—RV, provided that one of the variables W or V is N; Rt and Rw, if present, are H, halogen, methyl, C1-haloalkyl and the like; Ru and Rv, if present, are 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, S(O)mR2d, wherein m is 0, 1 or 2, R2a is C1-C4-alkyl, C1-C4-haloalkyl and the like, R2b, 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; and R1 is H, CN, C1-C10-alkyl and the like. The present invention further relates to a method for controlling invertebrate pests, to a method for protecting plant propagation material and/or the plants which grow therefrom, to plant propagation material, comprising at least one compound according to the present invention, to a method for treating or protecting an animal from infestation or infection by parasites and to an agricultural composition containing at least one compound according to the present invention.