Thermoplastic moulding materials consisting of(1) 70 to 99.9% by weight of a cellulose ester or cellulose mixed ester(2) 0.1 to 30% by weight of a rubber polymer built up in the form of blocks from recurring structural units (I) with molecular weights of 10,000 to 1,000,000--A--B-- IwhereinA denotes bifunctional polysiloxane segements of the formula--(R.sup.1)(R.sup.2)SiO--.sub.x IIin whichR.sup.1 and R.sup.2 =aryl (in particular phenyl) or alkyl (in particular methyl) andx is a number such that the molecular weight is .gtoreq.500, andB denotes bifunctional aliphatic polyester and/or aliphatic polyester segments with molecular weights of .gtoreq.800,and the glass transition temperatures of the polymeric blocks A and B are less than 20.degree. C., which contains additionally(3) 0 to 30% by weight based on the mixture of (1) and (2) of a plasticizer.