Mixtures of linear organopolysiloxanes of the general formula 1 for R3SiO—(SiR2O)n—SiR3  (1) are produced by a process in which organochlorosilanes of the general formula 2 R4−ySiCly  (2) where R is identical or different and is a hydrogen atom or an unsubstituted or substituted hydrocarbon radical having from 1 to 18 carbon atoms, Y is 1 or 2, and n is 0 or an integer from 1 to 50, are reacted continuously in a closed circulation system with water which may, if desired, have been acidified with hydrochloric acid, where the HCl concentration in the hydrochloric acid discharged is less than 25% by weight. Low molecular weight oligomer mixtures substantially free of both cyclic organosiloxanes and organosilicon compounds containing Si—Cl are economically produced.