The invention relates to polycyclic diiminooxadiazinones of the formula I and/or of the formula II, in which in each case R1 to R12 are each independently hydrogen, a saturated or unsaturated, linear or branched, aliphatic or cycloaliphatic organic radical having 1 to 20 carbon atoms, which is unsubstituted or is substituted by radicals inert to isocyanate groups, and/or comprises heteroatoms inert to isocyanate groups in the chain, or are an aromatic organic radical having 6 to 20 carbon atoms, which is unsubstituted or is substituted by radicals inert to isocyanate groups, wherein two or more of the aforementioned radicals R1 to R6 may form further rings, in each case with one another and incorporating one, two or three carbon atoms of the fused ring segment X, and/or two or more of the aforementioned radicals R7 to R12 may form further rings, in each case with one another and incorporating one, two or three carbon atoms of the fused ring segment Y.