Nitrogen-free anionic fabric softeners are provided by sulfated fatty acid partial glycerides corresponding fo formula (I): ##STR1## in which R.sup.1, R.sup.2 and R.sup.3 independently of one another represent at least one aliphatic, linear or branched acyl radical containing 6 to 22 carbon atoms, at least one sulfate group and optionally a hydroxyl group, and m, n and p=0 or a number from 1 to 10.