The present invention relates to N-acylimino compound of formula (I): (I) wherein X1 is O or S, in particular O; X2 is CN or NO2; m is an integer selected from 0, 1, 2, 3, 4, 5 and 6; Het is a 5- or 6- membered carbon-bound or nitrogen-bound heterocyclic or heteroaromatic ring, W1 is O, S or NRw1; W2-W3-W4 isa bivalent radical selected from -C(Rv2Rw2)-C(Rv3Rw3)-, -C(Rv4)=C(Rv5)- and - C(Rv2Rw2)-O-C(Rv3Rw3)-; R1, R2 may be hydrogen, halogen, etc. R3 may be hydrogen, halogen, CN, C1-C6-alkyl, etc. R4a, R4b if present, may be hydrogen, halogen, C1-C6-alkyl, etc. R5 may be hydrogen, halogen, C1-C6-alkyl, C1-C6-alkenyl, C1-C6-alkynyl, C3-C8- cycloalkyl, S(O)nNR9aR9b, NR9aR9b, C(=O)OR8, C(=O)NR9aR9b, C(=S)NR9aR9b, C(=O)R7a, C(=S)R7a, NR9a-C(=O)R7a, NR9a-C(=S)R7a, NR9a-S(O)nR8a, a moitey Q-phenyl, where the phenyl ring is optionally substituted with one or more, e.g. 1, 2, 3, 4 or 5 identical or different substituents R10, or a moiety Q-Het#, or R3 and R5 together may also form with the carbon atom they are bound to, a 3-, 4-, 5- or 6- membered saturated partially unsaturated carbocycle or heterocycle, wherein Rw1, Rw2, Rw3, Rv2, Rv3, Rv5, R7a, R8, R8a, R9a, R9b, Q, Het# are as defomed in the claims. The invention also relates to the use of the N-acylimino heterocyclic compounds, their stereoisomers, their tautomers and their salts, for combating invertebrate pests. Furthermore the invention relates also to methods of combating invertebrate pests, which comprises applying such compounds.