Polysiloxane sols preparable by subjecting (1) in a first stage (A) a silicon compound of the general formula I: (Z.sub.oL--).sub.mSi(H).sub.n(R).sub.p, (I) which is free of carbamate groups and where o is an integer from 1 to 5; m is 0, 1, 2 or 3; n is an integer from 1 to 4; p is 0, 1 , 2 or 3; Z is a reactive functional group, excluding carbamate group; L is an at least divalent, linking, organic group; H is a hydrolyzable, monovalent, organic group or hydrolyzable atom; R is a nonhydrolyzable, monovalent, organic group; to partial hydrolysis and condensation in the presence (B) of at least one crosslinking agent, and then subjecting (2) in a further stage, the reaction mixture (1) to complete hydrolysis and condensation with (C) a hydrolyzable, carbamate-functional silicon compound of the general formula II: {[HR.sup.1N--(O)C--O--].sub.rL--}.sub.sSi(H).sub.t(R).sub.u (II) where R.sup.1 is a hydrogen atom or group R; r is an integer from 1 to 5; s is 1, 2 or 3; t is 1, 2 or 3; u 0, 1 or 2; and their use as coating materials, adhesives, and sealing compounds and also for producing optical moldings and self-supporting films.