Fluoroalkyl- and fluoroaryl-group-containing imides and their salts of general formula (I) ##STR1## wherein R.sub.F is a fluoroalkyl group with 1 to 18 carbon atoms, a fluoroaryl group with 6 to 12 carbon atoms or a mixed fluoroalkylaryl group with 7 to 18 carbon atoms, wherein the carbon chain can also be interrupted by oxygen atoms,R.sub.H is an alkyl group with 1 to 30 carbon atoms, an aryl group with 6 to 12 carbon atoms or a mixed alkylaryl group with 7 to 30 carbon atoms, wherein the carbon chain of the group can also be interrupted by oxygen, nitrogen or sulphur atoms,Y.sub.1 and Y.sub.2 independently of each other represent a ##STR2## X is a hydrogen cation or a uni- or multivalent cation, m is a whole number from 0 to 6, andz is a whole number from 1 to 7 corresponding to the charge of the cation X.