The present invention relates to the use of substituted aryl- and heteroarylpropargylamines of the formula (I) ##STR00001## where a) R.sup.1 is heteroaryl or aryl, unsubstituted or mono- or polysubstituted by identical or different radicals, b) A is a group CR.sup.4R.sup.5 or C.dbd.O, where R.sup.4 is hydrogen, halogen or alkyl; R.sup.5 is hydrogen, halogen or a substituted or unsubstituted hydrocarbon radical; c) R.sup.2 and R.sup.3 together with the nitrogen atom to which they are attached form N-heteroaryl or N-heterocyclyl, unsubstituted or mono- or polysubstituted by identical or different radicals, if appropriate also as N-oxide or salt, as pesticide against arthropods and helminths for protecting plants and animals.