Quaternary siloxane polymers of the formula: ##STR1## in which A denotes an .alpha.,.beta.-bis-alkylpolysiloxane or a C.sub.1-6 hydrocarbon chain which can contain OH groups and can be interrupted by one or more oxygen atoms and/or aromatic rings; R.sub.1, R.sub.2, R.sub.3 and R.sub.4, which are identical or different, denote a C.sub.1 -C.sub.6 alkyl or phenyl; R.sub.5 =methyl, ethyl or --CH.sub.2 --; R.sub.6 =C.sub.1 -C.sub.18 alkyl or --CH.sub.2 --; if R.sub.5 and/or R.sub.6 denote --CH.sub.2 --, they form a methylpiperazinium radical or ethylpiperazinium radical, a diethylenediamine radical or a heterocycle with --N--A--N--; Y denotes one of the anions Cl.sup.-, Br.sup.-, CH.sub.3 SO.sub.3.sup.-, ##STR2## m=1-6; and p=1-50 are disclosed for use, in particular, for treating the hair, nails and skin. They are resistant to several rinses on these substrates.