.alpha.-arylacrylic acid derivatives, their preparation and their use for controlling pests and fungi

A method for controlling insects, arachnids or nematodes, wherein the insects, arachnids or nematodes or their habitat are or is treated with an effective amount of an .alpha.-arylacrylic acid derivative of the formula I' ##STR13## wherein X is ethylene or ethenylene;

• Y is a direct bond or oxygen;
• R.sup.1 is a mononuclear or dinuclear aromatic system which is bonded via a carbon atom, and this aromatic system is optionally substituted by from one to seven halogen atoms or from one to four of the following radicals;
• C.sub.1 -C.sub.4 -alkyl, C.sub.1 -C.sub.4 -haloalkyl, C.sub.1 -C.sub.4 -alkoxy, C.sub.1 -C.sub.4 -haloalkoxy, C.sub.1 -C.sub.4 -alkylthio, C.sub.1 -C.sub.4 - haloalkylthio, C.sub.3 -C.sub.6 -cycloalkyl, C.sub.5 - or C.sub.6 -cycloalkenyl, C.sub.2 -C.sub.4 -alkenyl or C.sub.2 -C.sub.4 -alkynyl or from one to three cyano or nitro substituents;
• R.sup.2 is cyano, nitro, halogen, C.sub.1 -C.sub.4 -alkyl, C.sub.1 -C.sub.4 -haloalkyl, C.sub.1 -C.sub.4 -alkoxy, C.sub.1 -C.sub.4 -haloalkoxy, C.sub.1 -C.sub.4 -alkythio, or C.sub.1 -C.sub.4 -haloalkythio;
• n is 1 or 2, and the substituents are identical or different if n is 2, and
• m is 0, 1 or 2, and the substituents are identical or different if
• m is 2, with the proviso that R.sup.1 is not phenyl when X is ethylene,
• X is oxygen, p is 1 and m is 0.