Hydrophilic siloxane copolymers are prepared by(a) reacting organopolysiloxanes having at least one Si-bonded hydrogen atom with substantially linear oligomeric or polymeric compounds of formulaR1-(A-CnH2n)m-A1-H (I)where R1 is a monovalent optionally substituted, hydrosilylatable hydrocarbyl radical,A is a bivalent polar organic radical selected from —O—, —C(O)—O—, —O—C(O)—, —O—C(O)—O—, —C(O)—NH—, —NH—C(O)—, urethane radicals and urea radicals,A1 is a bivalent polar organic radical selected from —O—, —NH— and —NR′—, n is an integer from 1 to 20, and m is zero or a positive integer,(b) reacting the resulting intermediate with organic compounds which have two or more isocyanate groups, in the presence of further organic compounds (6) reactive toward isocyanate groups and containing at least one tertiary amine group, and(c) quaternizing the amino-group-containing intermediate from step (b) with an alkylating agent (8),with the proviso that the water content of the compounds (1) and (2) is lower than 2000 weight ppm.