A method of combating arthropods and nematodes which comprises applying thereto, to a habitat thereof or to an area from which they are to be excluded an arthropodicidally or nematocidally effective amount of at least one long-chain halogenoolefine of the formula (I) ##STR1## in which R represents a straight-chain or branched alkyl radical with 8 to 25 carbon atoms in the straight chain, the alkyl radical optionally being interrupted once or several times by a --C.tbd.C-- and/or ##STR2## in which Z and Z.sup.1 are identical or different and represent hydrogen or methyl andR.sup.1 represents hydrogen, alkyl or halogen.Those compounds are new wherein R has at least 12 carbon atoms in the straight chain.