The present invention relates to N-acylimino compound of formula (I): wherein X is O or S, in particular O; m is an integer selected from 0, 1, 2, 3, 4, 5 or 6; Het is a 5 or 6 membered carbon-bound or nitrogen-bound heterocyclic ring, W1-W2-W3-W4 represents a carbon chain group connected to N and C═N, and thus forming a saturated, unsaturated, or partially unsaturated 5 or 6 membered nitrogen containing heterocycle, wherein W1, W2, W3 and W4 each individually represent CRvRw, 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-alkinyl, 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. 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.