The present invention relates to succinimides of the formula I ##STR1## in which R.sup.1 and R.sup.2, independently of one another, are hydrogen, C.sub.1 -C.sub.24 -alkyl, C.sub.2 -C.sub.24 -alkenyl, C.sub.6 -C.sub.12 -cycloalkyl, C.sub.6 -C.sub.12 -cycloalkenyl, C.sub.6 -C.sub.12 -aryl, C.sub.1 -C.sub.24 -alkoxy, C.sub.1 -C.sub.24 -acyl, C.sub.1 -C.sub.24 -acyloxy, a hydroxyl, amino or sulfo group or a C.sub.1 -C.sub.24 -dialkylamino, C.sub.1 -C.sub.24 -acylamino, C.sub.1 -C.sub.24 -alkylsulfato, C.sub.1 -C.sub.24 -alkylsulfonato, C.sub.1 -C.sub.24 -alkylsulfito, C.sub.1 -C.sub.24 -alkylsulfinyl or C.sub.1 -C.sub.24 -alkoxycarbonyl radical, and R.sup.3 is a polyhydroxyalkyl radical of the formula ##STR2## in which R.sup.4 is --(CHOR.sup.7).sub.n --H, R.sup.5 is --(CHOR.sup.7).sub.m --H, R.sup.6 is --(CHOR.sup.7).sub.o --H where n+m+o is 2-6, and R.sup.7 is H or a carbohydrate attached in the form of a glycoside from the series comprising reducing sugars, a process for their preparation and their use.