The subject-matter of the invention is a process for the preparation of silicone oils which are weakly colored and low in turbidity by hydrosilylation of polyorganohydrosiloxanes with different or identical synthons comprising at least one hydrocarbon-comprising ring in which is included an oxygen atom, the said reaction being carried out in the presence of a heterogeneous catalytic composition comprising a metal chosen from the group consisting of cobalt, rhodium, ruthenium, platinum and nickel deposited on an inert support.