Process for conditioning textile materials in order to enable them to have, especially, a pleasant handle and a very low or even non-existent yellowing, characterized in that the textile materials are brought into contact with a composition comprising a polyorganosiloxane having, per mole, at least one unit of general formula: ##EQU1## in which: R can represent a C.sub.1 -C.sub.4 alkyl radical;X can represent a hydrolysable radical;Z represents a residue containing (a) sterically hindered piperidyl group(s) of formulae: ##STR1## in which R.sup.1 is a divalent hydrocarbon radical, R'.sup.1 is a trivalent hydrocarbon radical, U and U' represent --O--, --NH-- or --N(alkyl)--, R.sup.2 can represent a C.sub.1 -C.sub.3 alkyl radical and R.sup.3 is H or R.sup.2,a and b are chosen from 0, 1 and 2,the sum a+b being not greater than 2.