Highly functionalized polyurethanes

A process for preparing highly functionalized polyurethanes, which comprises adding, to an initiator core having at least 2 functional groups B', a molecule containing the functional groups A(B).sub.n to each functional group B', where A is an NCO group or a group reactive with an NCO group, B and B' are an NCO group or a group reactive with an NCO group, A is reactive with B and B' and n is a positive number and is at least equal to 2, wherein the addition the functional groups B of the molecule to be added are converted into a form in which they cannot react with A, after the addition the functional groups B are again converted into the form reactive with A, in the same manner in turn a molecule containing the functional groups A(B).sub.n is added to each reactive group B and the process is continued until the desired functionality is achieved or an addition of further molecules is no longer possible for steric or other reasons.