Compounds containing carbon-carbon double bonds and/or carbon-carbon triple bonds are hydrosilylated with linear organopolysiloxanes having diorganosiloxy units and Si—H groups, produced by reacting diorganodichlorosilanes and monochlorosilanes and optionally dichlorosilanes with water in a first step, where at least one of the monochlorosilanes or dichlorosilanes contain Si—H groups to give a partial hydrolysate and gaseous hydrogen chloride, and in a second step, treating the partial hydrolysate with water to remove SiCl groups still present to form hydrochloric acid, and producing a hydrolysate containing the organopolysiloxanes.