The invention discloses a method for the preparation of an organopolysiloxane having a branched molecular structure which comprises the steps of: (A) Mixing (A1) an organopolysiloxane represented by the average unit formula [R13SiO½]m[R1SiO{fraction (3/2)}]n[R1(R2O)SiO]q, in which R1 is a monovalent hydrocarbon group, R2 is a hydrogen atom, methyl group or ethyl group and the subscripts m, n and q are each 0 or a positive number with the proviso that (n+q)/m is from 0.6 to 1.5 and q/(m+n) is 0 or a positive number not exceeding 0.05; (A2) a cyclic dialkylsiloxane oligomer, and (A3) a polyorganosiloxane represented by the structural formula R33Si—O—(—SiR32—O—)r—SiR33, In which R3 is a monovalent hydrocarbon group and the subscript r is 0 or a positive integer not exceeding 100, to give a siloxane mixture; (B) admixing the siloxane mixture with an alkaline compound; and (C) heating the siloxane mixture to effect siloxane rearrangement polymerization of the organopolysiloxanes.