Arylalkoxycoumarins of the general formula I ##STR1## where R.sup.1 and R.sup.2 independently of one another are each hydrogen, lower alkyl, phenyl or halogen, or the two radicals together form an alkylene bridge of 3 to 5 carbon atoms, R.sup.3 is lower alkyl or halogen, n is an integer of from 0 to 3, m is an integer of from 0 to 4, R.sup.4 is hydrogen or lower alkyl and Ar is a phenyl ring which is monosubstituted to trisubstituted by halogen, C.sub.1 -C.sub.6 -alkyl or C.sub.1 -C.sub.6 -alkoxy or monosubstituted by nitro, cyano or trifluoromethyl or is a naphthyl ring, with the proviso that m is not 0 when Ar is unsubstituted phenyl, processes for their preparation, and drugs prepared therefrom.