The present invention relates to N-acylimino compound of formula (I): wherein X is O or S, in particular O; Y is a single bond, O, S or NR5; 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, CN, C1-C6-alkyl, etc.; R4 may be of hydrogen, C1-C6-alkyl, C2-C6-alkenyl, C2-C6-alkinyl, C3-C8-cycloalkyl, Q-phenyl, Q′-O-phenyl, Q′-S-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, and the moieties Q-Het#, Q′-O-Het# and Q′-S-Het# where Het# represents a heterocyclic radical and where Q and Q′ are C1-C6-alkandiyl, C2-C6-alkendiyl, or C2-C6-alkyndiyl, and where Q may also be a single bond; R3 and R4 together may also may also a bivalent radical, selected from the group consisting of C2-C5-alkandiyl, C2-C5-alkendiyl, Q″-C1-C4-alkandiyl and Q″-C2-C4-alkendiyl, where Q″ is O or S. 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.